All my papers by field
Connectivity
 Tangles in the social sciences, preprint 2019; PDF
 Structural submodularity and tangles in abstract separation
systems (with J. Erde & D. Weißauer), JCTA 167C (2019),
155180; PDF
 Profinite separation systems (with J. Kneip), to appear in
Order; short/long
version
 Abstract separation systems, Order
35 (2018), 157170; PDF
 Tangletree duality in abstract separation systems (with S.
Oum), preprint 2017; PDF.
 Duality theorems for blocks and tangles in graphs (with J.
Erde & Ph. Eberenz), SIDMA 31 (2017) 15141528, PDF

Tangles and the Mona Lisa (with G. Whittle), preprint 2016; PDF
 Tangletree duality: in graphs, matroids and beyond (with S.
Oum), Combinatorica 39 (2019), 879910; PDF.
 Profiles of separations: in graphs, matroids and beyond (with
F. Hundertmark & S. Lemanczyk), Combinatorica 39 (2019), 37–75;
PDF
 Connected treewidth (with M. Müller), Combinatorica 38
(2018), 381398; PDF
 Canonical treedecompositions of finite graphs I. Existence
and algorithms (with J. Carmesin, M. Hamann & F.
Hundertmark), J. Combin. Theory (Series B) 116 (2016), 124; PDF.
 Canonical treedecompositions of finite graphs II. Essential
parts (with J. Carmesin, M. Hamann & F. Hundertmark), J.
Combin. Theory (Series B) 118 (2016), 268283; PDF.
 kBlocks: a connectivity invariant for graphs (with J.
Carmesin, M. Hamann & F. Hundertmark), SIDMA 28 (2014),
18761891; PDF.
 Connectivity and treestructure in finite graphs (with J.
Carmesin, F. Hundertmark & M. Stein), Combinatorica 34
(2014), 135; PDF.
Finite graph minors
 Tangletree duality: in graphs, matroids and beyond (with S.
Oum), Combinatorica 39 (2019), 879910; PDF.
 Duality theorems for blocks and tangles in graphs (with J.
Erde & Ph. Eberenz), SIDMA 31 (2017) 15141528, PDF
 Profiles of separations: in graphs, matroids and beyond (with
F. Hundertmark & S. Lemanczyk),
Combinatorica 39 (2019), 37–75; PDF
 Tree sets, Order 35 (2018), 171192; PDF
 Unifying duality theorems for width parameters I. Weak
and strong duality (with S. Oum), preprint 2014; PDF.
 Unifying duality theorems for width parameters II.
General duality (with S. Oum), preprint 2014; PDF.
 The ErdösPósa property for clique minors in highly connected
graphs (with K. Kawarabayashi & P. Wollan), J. Combin.
Theory (Series B) 102 (2012), 454469; PDF.
 On the excluded minor structure theorem for graphs of large
treewidth (with K. Kawarabayashi, T. Müller & P.
Wollan), J. Combin. Theory (Series B) 102 (2012),
11891210; PDF.
 Graph minor hierarchies (with D. Kühn), Discrete Applied
Mathematics 145 (2005), 167182; abstract; PDF
 Dense minors in graphs of large girth (with C. Rempel),
Combinatorica 25 (2005), 111116; abstract; PDF
 Two short proofs concerning treedecompositions (with P.
Bellenbaum), Combinatoric, Probability and Computing 11 (2002),
17; abstract; PDF
 Highly connected sets and the excluded grid theorem (with
K.Yu. Gorbunov, T.R. Jensen and C. Thomassen), J. Combin. Theory
(Series B) 75 (1999), 6173; abstract; DVI (A better exposition with figures
is available in the chapter on
graph minors in Graph Theory, 2nd ed'n.)
 Graph Minors I: a short proof of the pathwidth theorem,
Combinatorics, Probability and Computing 4 (1995), 2730; DVI (A better exposition with
figures is available here in PDF
 an excerpt from the chapter on graph minors in Graph
Theory, 1st ed'n.)
Infinite graph minors
 Ends and tangles, Abhandlungen Math. Sem. Univ. Hamburg 87
(2017), Special volume in memory of Rudolf Halin, 223244; PDF.
 Forcing finite minors in sparse infinite graphs by
largedegree assumptions, Electronic J. Comb. 22 (2015), #P1.43;
PDF
 A short proof of Halin's grid theorem, Abh. Math. Sem. Univ.
Hamburg 74 (2004), 137242; abstract; PDF
 An accessibility theorem for infinite graph minors, J. Graph
Theory 35 (2000), 273277; abstract; DVI; PDF
 Normal spanning trees, Aronszajn trees and excluded minors
(with I. Leader), J. London Math. Soc. 63 (2001), 1632; abstract; PDF
 A universal planar graph under the minor relation (with D.
Kühn), J. Graph Theory 32 (1999), 191206; abstract; PDF
 Excluding a countable clique (with R. Thomas), J. Combin.
Theory (Series B) 76 (1999), 4167; abstract; PDF
 The depthfirst search tree structure of TKomegafree
graphs,
J.
Combin.
Theory
(Series
B)
61
(1994),
260262.
DVI
 The structure of TKafree graphs, J. Combin. Theory (Series B)
54 (1992), 222238. PDF
 Simplicial minors and decompositions of graphs, Math. Proc.
Camb. Phil. Soc. 103 (1988), 409426. DVI
 On universal graphs with forbidden topological subgraphs,
Europ. J. Combinatorics 6 (1985), 175182.
 On the problem of finding small subdivision and homomorphism
bases for classes of countable graphs, Discrete Mathematics 55
(1985), 2133.
Topological aspects of infinite graphs
 Ends and tangles, Abhandlungen Math. Sem. Univ. Hamburg
(Volume in memory of Rudolf Halin), 2017; PDF
 Orthogonality and minimality in the homology of locally finite
graphs (with J. Pott), Electronic J. Comb. 21 (2014), #P3.36; PDF.
 Dual trees must share their ends (with J. Pott),
J. Combin. Theory (Series B) 123 (2017) 3253; PDF
 On the homology of locally compact spaces with ends (with P.
Sprüssel), Topology and its Applications 158 (2011), 16261639;
PDF
 Locally finite graphs with ends: a topological approach I–III
(survey), Discrete Math 311–312 (2010–11); PDF
 The homology of locally finite graphs with ends (with P.
Sprüssel), Combinatorica 30 (2010), 681714; abstract; PDF
 End spaces and spanning trees, J. Combin. Theory (Series B) 96
(2006), 846854; abstract;
DVI; PDF
 Duality in infinite graphs (with H. Bruhn), Comb. Probab.
Computing 15 (2006), 7590; abstract; PDF
 Cyclecocycle partitions and faithful cycle covers for locally
finite graphs (with H. Bruhn & M. Stein), J.
Graph Theory 50 (2005), 150161; abstract; PDF
 The cycle space of an infinite graph, Combinatorics,
Probability and Computing 14 (2005), 5979; abstract; PDF
 Graphtheoretical versus topological ends of graphs (with D.
Kühn), J. Combin. Theory (Series B) 87 (2003), 197206; abstract; PDF
 Topological paths, cycles and spanning trees in infinite
graphs (with D. Kühn), Europ. J. Combinatorics 25 (2004),
835862; abstract; PDF
 On infinite cycles I (with D. Kühn), Combinatorica 24 (2004),
6889; abstract; PDF
 On infinite cycles II (with D. Kühn), Combinatorica 24 (2004),
91116; abstract;
PDF
Growth in infinite graphs
 The classification of finitely spreading graphs, Proc. London
Math. Soc (3) 73 (1996), 534554. PDF
 Dominating functions and graphs (with S. Shelah and J.
Steprans), J. London Math. Soc 49 (1994) 1624. DVI
 The growth of infinite graphs (with I. Leader): boundedness
and finite spreading, Combinatorics, Probability and Computing 3
(1994) 5155. DVI; PDF
 Dominating functions and topological graph minors,
Contemporary Mathematics 147 (1993), 461476. PDF
 A proof of the Bounded Graph Conjecture (with I. Leader),
Invent. math. 108 (1992), 131162; abstract; download: DVI; PDF
Normal spanning trees
 A simple existence criterion for normal spanning trees in
infinite graphs, Electronic J. Comb. 23 (2016), #P2.33; PDF.
 End spaces and spanning trees, J. Combin. Theory (Series B) 96
(2006), 846854; abstract;
DVI; PDF
 Normal spanning trees, Aronszajn trees and excluded minors
(with I. Leader), J. London Math. Soc 63 (2001), 1632; abstract; PDF
 Normal tree orders for infinite graphs (with J.M. Brochet),
Trans. Amer. Math. Soc 345 (1995), 871895. DVI
 The depthfirst search tree structure of TKomegafree
graphs,
J.
Combin.
Theory
(Series
B)
61
(1994),
260262.
DVI
Treedecompositions and generalizations
 Structural submodularity and tangles in abstract separation
systems (with J. Erde & D. Weißauer), JCTA 167C (2019),
155180; PDF
 Profinite separation systems (with J. Kneip), preprint 2018; short/long
version
 Tree sets, Order 35 (2018), 171192; PDF
 Tangletree duality in abstract separation systems (with S.
Oum), preprint 2017; PDF.
 Tangletree duality: in graphs, matroids and beyond (with S.
Oum), Combinatorica 39 (2019), 879910; PDF.
 Profiles of separations: in graphs, matroids and beyond (with
F. Hundertmark & S. Lemanczyk),
Combinatorica 39 (2019), 37–75; PDF
 Connected treewidth (with M. Müller),
Combinatorica 38 (2018), 381398; PDF
 Unifying duality theorems for width parameters I. Weak
and strong duality (with S. Oum), preprint 2014; PDF.
 Unifying duality theorems for width parameters II.
General duality (with S. Oum), preprint 2014; PDF.
 Canonical treedecompositions of finite graphs I. Existence
and algorithms (with J. Carmesin, M. Hamann & F.
Hundertmark),
JCTB 116 (2016), 124; PDF.
 Canonical treedecompositions of finite graphs II. Essential
parts (with J. Carmesin, M. Hamann & F. Hundertmark),
J. Combin. Theory (Series B) 118 (2016), 268283; PDF.
 Connectivity and treestructure in finite graphs (with J.
Carmesin, F. Hundertmark & M. Stein), Combinatorica 34
(2014), 135; PDF.
 Graph minor hierarchies (with D. Kühn), Discrete Applied
Mathematics 145 (2005), 167182; abstract; PDF
 Decomposition duality (generalizes treedecompositions;
manuscript 2002); abstract;
DVI; PDF
 Two short proofs concerning treedecompositions (with P.
Bellenbaum), Combinatoric, Probability and Computing 11 (2002),
17; abstract; PDF
 Highly connected sets and the excluded grid theorem (with
K.Yu. Gorbunov, T.R. Jensen and C. Thomassen), J. Combin. Theory
(Series B) 75 (1999), 6173; abstract; DVI (A better exposition with figures
is available in the chapter on
graph minors in Graph Theory, 2nd ed'n.)
 Excluding a countable clique (with R. Thomas), J. Combin.
Theory (Series B) 76 (1999), 4167; abstract; PDF
 The depthfirst search tree structure of TKomegafree
graphs,
J.
Combin.
Theory
(Series
B)
61
(1994),
260262.
DVI
 On spanning trees and kconnectedness in infinite graphs, J.
Combin. Theory (Series B) 56 (1992), 263277. DVI
 Treedecompositions, treerepresentability and chordal graphs,
Discrete Mathematics 71 (1988), 181184. DVI
Ends of graphs
 Ends and tangles,
Abhandlungen Math. Sem. Univ. Hamburg (Volume in memory of
Rudolf Halin), 2017; PDF
 Dual trees must share their ends (with J. Pott), J. Combin.
Theory (Series B) 123 (2017) 3253; PDF
 Forcing finite minors in sparse infinite graphs by
largedegree assumptions, Electronic J. Comb. 22 (2015), #P1.43;
PDF
 The fundamental group of a locally finite graph with ends
(with P. Sprüssel), Adv. Math 226 (2011), 26432675; abstract; PDF.
 The homology of locally finite graphs with ends (with P.
Sprüssel), Combinatorica 30 (2010), 681714; abstract; PDF.
 End spaces and spanning trees, J. Combin. Theory (Series B) 96
(2006), 846854; abstract;
DVI; PDF
 Menger's theorem for infinite graphs with ends (with
H. Bruhn & M. Stein), J. Graph Theory 50
(2005), 199211; abstract; DVI; PDF
 A short proof of Halin's grid theorem, Abh. Math. Sem. Univ.
Hamburg 74 (2004), 137242; abstract; PDF
 Duality in infinite graphs (with H. Bruhn), Combinatoric,
Probability and Computing 15 (2006), 7590; abstract; PDF
 Cyclecocycle partitions and faithful cycle covers for locally
finite graphs (with H. Bruhn & M. Stein), J.
Graph Theory 50 (2005), 150161; abstract; PDF
 The ErdösMenger conjecture for source/sink sets with disjoint
closures, J. Comb. Theory (Series B) 93 (2005), 107114; abstract; DVI; PDF
 The cycle space of an infinite graph, Combinatorics,
Probability and Computing 14 (2005), 5979; abstract; PDF
 The countable ErdösMenger conjecture with ends, J. Combin.
Theory (Series B) 87 (2003), 145161; abstract; PDF
 Graphtheoretical versus topological ends of graphs (with D.
Kühn), J. Combin. Theory (Series B) 87 (2003), 197206; abstract; PDF
 Topological paths, cycles and spanning trees in infinite
graphs (with D. Kühn), Europ. J. Combinatorics 25 (2004),
835862; abstract; PDF
 On infinite cycles I (with D. Kühn), Combinatorica 24 (2004),
6889; abstract; PDF
 On infinite cycles II (with D. Kühn), Combinatorica 24 (2004),
91116; abstract;
PDF
 Normal tree orders for infinite graphs (with J.M. Brochet),
Trans. Amer. Math. Soc 345 (1995), 871895. DVI
 The depthfirst search tree structure of TKomegafree
graphs,
J.
Combin.
Theory
(Series
B)
61
(1994),
260262.
DVI
 On vertex transitive graphs of infinite degree (with H.A. Jung
and R. Möller), Arch. Math. 60 (1993), 591600. DVI
 The end structure of a graph, Discrete Mathematics 100 (1992),
313327. DVI
 On spanning trees and kconnectedness in infinite graphs, J.
Combin. Theory (Series B) 56 (1992), 263277. DVI
 On endfaithful spanning trees in infinite graphs, Math. Proc.
Camb. Phil. Soc. 107 (1990), 461473. PDF
ErdösMenger conjecture; paths in infinite graphs
 A CantorBernstein theorem for paths in graphs (with C.
Thomassen), Amer. Math. Monthly 113 (2006), 161166; abstract; PDF
 Menger's theorem for infinite graphs with ends (with
H. Bruhn & M. Stein), J. Graph Theory 50
(2005), 199211; abstract; DVI; PDF
 The ErdösMenger conjecture for source/sink sets with disjoint
closures, J. Comb. Theory (Series B) 93 (2005), 107114; abstract; DVI; PDF
 The countable ErdösMenger conjecture with ends, J. Combin.
Theory (Series B) 87 (2003), 145161; abstract; PDF
 Menger's theorem for a countable source set (with R. Aharoni),
Combinatorics, Probability and Computing 3 (1994), 145156; DVI
 A proof of the ErdösMenger conjecture for countably connected
graphs without large simplices, preprint 1988. DVI (subsumed in Graph
Decompositions)
Algebraic graph theory
 Structural submodularity and tangles in abstract separation
systems (with J. Erde & D. Weißauer), JCTA 167C (2019),
155180; PDF
 Profinite separation systems (with J. Kneip), to appear in
Order; short/long
version
 Abstract separation systems, Order 35 (2018), 157170; PDF
 Tangletree duality: in graphs, matroids and beyond (with S.
Oum), Combinatorica 39 (2019), 879910; PDF.
 Profiles of separations: in graphs, matroids and beyond (with
F. Hundertmark & S. Lemanczyk),
Combinatorica 39 (2019), 37–75; PDF
 Orthogonality and minimality in the homology of locally finite
graphs (with J. Pott), Electronic J. Comb. 21 (2014), #P3.36; PDF.
 The homology of locally finite graphs with ends (with P.
Sprüssel), Combinatorica 30 (2010), 681714; abstract; PDF
 MacLane's theorem for arbitrary surfaces (with H. Bruhn),
J. Combin. Theory (Series B) 99 (2009) 275286; abstract; short; extended
 Duality in infinite graphs (with H. Bruhn), Combinatoric,
Probability and Computing 15 (2006), 7590; abstract; PDF
 The cycle space of an infinite graph, Combinatorics,
Probability and Computing 14 (2005), 5979; abstract; PDF
 On infinite cycles I (with D. Kühn), Combinatorica 24 (2004),
6889; abstract; PDF
 On infinite cycles II (with D. Kühn), Combinatorica 24 (2004),
91116; abstract;
PDF
 A conjecture concerning a limit of nonCayley graphs (with I.
Leader), J. Algebraic Combinatorics 14 (2001), 1725; abstract; PDF
 On vertex transitive graphs of infinite degree (with H.A. Jung
and R. Möller), Arch. Math. 60 (1993), 591600. DVI
Extremal graph theory
 Global connectivity and expansion: long cycles and factors in
fconnected graphs (with St. Brandt, H. Broersma, & M.
Kriesell), Combinatorica 26 (2006), 1736; abstract; PDF
 Dense minors in graphs of large girth (with C. Rempel),
Combinatorica 25 (2005), 111116; abstract; PDF
Planar graphs and graphs in surfaces
 MacLane's theorem for arbitrary surfaces (with H. Bruhn),
J. Combin. Theory (Series B) 99 (2009) 275286; abstract; short; extended
 Duality in infinite graphs (with H. Bruhn), Comb. Probab.
Computing 15 (2006), 7590; abstract; PDF
 A universal planar graph under the minor relation (with D.
Kühn), J. Graph Theory 32 (1999), 191206; abstract; PDF
 Excluding a countable clique (with R. Thomas), J. Combin.
Theory (Series B) 76 (1999), 4167; abstract; PDF
 A separation property of planar triangulations, J. Graph
Theory 11 (1987), 4352.55 (1985), 2133.
Simplicial decompositions
 Decomposing infinite graphs, Discrete Mathematics 95 (1991),
6989. PDF (Expository
introduction to Graph
Decompositions)
 A compactness theorem for complete separators, Abh. Math. Sem.
Univ. Hamburg 60 (1990), 149151. DVI
 Simplicial minors and decompositions of graphs, Math. Proc.
Camb. Phil. Soc. 103 (1988), 409426. DVI
 Simplicial treedecompositions of infinite graphs I, J.
Combin. Theory (Series B) 48 (1990), 197215. DVI
 Simplicial treedecompositions of infinite graphs II  the
existence of prime decompositions, J. Combin. Theory (Series B)
50 (1990), 93116. DVI
 Simplicial treedecompositions of infinite graphs III  the
uniqueness of prime decompositions, J. Combin. Theory (Series B)
50 (1990), 117128. DVI
 Simplicial decompositions of graphs  a survey of
applications, Discrete Mathematics 75 (1989), 121144. DVI
 Simplicial decompositions, treedecompositions and graph
minors, Ars Combinatoria 25C (1988), 97104. DVI;
PDF
 Decompositions of infinite graphs into small induced
subgraphs, preprint 1987. DVI
 Simplicial decompositions of graphs  some uniqueness results,
J. Combin. Theory (Series B) 42 (1987), 133145.
 A separation property of planar triangulations, J. Graph
Theory 11 (1987), 4352.
Universal graphs
 A universal planar graph under the minor relation (with D.
Kühn), J. Graph Theory 32 (1999), 191206; abstract; PDF
 Some remarks on universal graphs (with R. Halin and W.
Vogler), Combinatorica 5 (1985), 283293.
 On the problem of finding small subdivision and homomorphism
bases for classes of countable graphs, Discrete Mathematics 55
(1985), 2133.
 On universal graphs with forbidden topological subgraphs,
Europ. J. Combinatorics 6 (1985), 175182.
Matroids
 Tangletree duality: in graphs, matroids and beyond (with S.
Oum), Combinatorica 39 (2019), 879910; PDF.
 Profiles of separations: in graphs, matroids and beyond (with
F. Hundertmark & S. Lemanczyk),
Combinatorica 39 (2019), 37–75; PDF
 The structure of 2separations of infinite matroids (with E.
AignerHorev & L. Postle),
J. Combin. Theory (Series B) 116 (2016), 2556; PDF
 Infinite matroids in graphs (with H. Bruhn), in the Infinite Graph Theory
special volume of Discrete Math 311 (2011), 14611471; PDF
 Axioms for infinite matroids (with H. Bruhn, M. Kriesell, R.
Pendavingh & P. Wollan), Adv. Math 239 (2013), 1846; PDF
Infinite combinatorics, orders and logic

Profinite separation systems (with J. Kneip), preprint 2018; short/long
version
 Tree sets,
Order 35 (2018), 171192; PDF
 Twins of rayless graphs (with A. Bonato, H. Bruhn & P.
Sprüssel), J. Combin. Theory (Series B) 101 (2011) 6065; PDF.
 Every rayless graph has an unfriendly partition (with H.
Bruhn, A. Georgakopoulos & P. Sprüssel), Combinatorica 30
(2010), 521532; DVI, PDF.
 Orientations and partitions of the Rado graph (with I. Leader,
A. Scott & St. Thomassé), Trans. Amer. Math. Soc 359 No.5
(2007), 23952405; abstract;
DVI; PDF
 A CantorBernstein theorem for paths in graphs (with C.
Thomassen), Amer. Math. Monthly 113 (2006), 161166; abstract; PDF
 On the cofinality of infinite partially ordered sets:
factoring a poset into lean essential subsets (with O.
Pikhurko), Order 20 (2003), 5366; abstract; DVI; PDF
 Relating subsets of a poset, and a partition theorem for WQOs,
Order 18 (2001), 275279; abstract; DVI; PDF
 Normal spanning trees, Aronszajn trees and excluded minors
(with I. Leader), J. London Math. Soc 63 (2001), 1632; abstract; PDF
 An accessibility theorem for infinite graph minors, J. Graph
Theory 35 (2000), 273277; abstract DVI; PDF
 Normal tree orders for infinite graphs (with J.M. Brochet),
Trans. Amer. Math. Soc 345 (1995), 871895; DVI
 Domination games on infinite graphs (with I. Leader), Theor.
Computer Science A 132 (1994), 337345; PDF
 Dominating functions and graphs (with S. Shelah and J.
Steprans), J. London Math. Soc 49 (1994) 1624; DVI
Topology
 Ends and tangles, Abhandlungen Math. Sem. Univ. Hamburg 87
(2017), Special volume in memory of Rudolf Halin, 223244; PDF
 On the homology of locally compact spaces with ends (with P.
Sprüssel), Topology and its Applications 158 (2011), 16261639;
PDF
 The fundamental group of a locally finite graph with ends
(with P. Sprüssel), Adv. Math 226 (2011), 26432675; abstract; PDF.
 The homology of locally finite graphs with ends (with P.
Sprüssel), Combinatorica 30 (2010), 681714; abstract; PDF.
Applications outside mathematics
 Tangles in the social sciences, preprint 2019; PDF
 Tangles and the Mona Lisa (with G. Whittle), preprint 2016; PDF
Technical note:
My DVI files do not contain figures. For this reason, I try to
post papers that include figures in PDF. Thus, papers posted in
DVI either contain no figures or are too old for proper conversion
into PDF. In some such (pre1995) cases I managed to produce PDF
files with partial figures, which are also posted above.
Home