Reinhard Diestel's papers

All my papers by field

Connectivity

A structural duality for path-decompositions into parts of small radius (S. Albrechtsen, R. Diestel, A. Elm, E. Fluck, R. Jacobs, P. Knappe and P. Wollan), preprint 2023; ArXiv
A grid theorem for strong immersions of walls (R. Diestel, R. Jacobs, P. Knappe and P. Wollan), preprint 2023; ArXiv
Canonical graph decompositions via coverings (with R. Jacobs, P. Knappe and J. Kurkofka), preprint 2022; ArXiv
Point sets and functions inducing tangles of set separations (with C. Elbracht & R. Jacobs), J. Combinatorics (to appear in 2024); ArXiv
Duality and tangles of set separations (with C. Elbracht, Joshua Erde & M. Teegen), J. Combinatorics 15 (2024), 1–39; ArXiv
Profinite separation systems (with J. Kneip), Order 37 (2020), 179-205; short/long version
Tangles in the social sciences, preprint 2019 (superseded by tangles book); PDF
Structural submodularity and tangles in abstract separation systems (with J. Erde & D. Weißauer), JCTA 167C (2019), 155-180; PDF
Abstract separation systems, Order 35 (2018), 157-170; PDF
Tangle-tree duality in abstract separation systems (with S. Oum), to appear in Adv.Math 377 (2021); PDF.
Duality theorems for blocks and tangles in graphs (with J. Erde & Ph. Eberenz), SIDMA 31 (2017) 1514-1528, PDF
Tangles and the Mona Lisa (with G. Whittle), preprint 2016; PDF
Tangle-tree duality: in graphs, matroids and beyond (with S. Oum), Combinatorica 39 (2019), 879-910; PDF.
Profiles of separations: in graphs, matroids and beyond (with F. Hundertmark & S. Lemanczyk), Combinatorica 39 (2019), 37–75; PDF
Connected tree-width (with M. Müller), Combinatorica 38 (2018), 381-398; PDF
Canonical tree-decompositions of finite graphs I. Existence and algorithms (with J. Carmesin, M. Hamann & F. Hundertmark), J. Combin. Theory (Series B) 116 (2016), 1-24; PDF.
Canonical tree-decompositions of finite graphs II. Essential parts (with J. Carmesin, M. Hamann & F. Hundertmark), J. Combin. Theory (Series B) 118 (2016), 268-283; PDF.
k-Blocks: a connectivity invariant for graphs (with J. Carmesin, M. Hamann & F. Hundertmark), SIDMA 28 (2014), 1876-1891; PDF.
Connectivity and tree-structure in finite graphs (with J. Carmesin, F. Hundertmark & M. Stein), Combinatorica 34 (2014), 1-35; PDF.

Finite graph minors

A structural duality for path-decompositions into parts of small radius (with S. Albrechtsen, A. Elm, E. Fluck, R. Jacobs, P. Knappe and P. Wollan), preprint 2023; ArXiv
A grid theorem for strong immersions of walls, (with R. Jacobs, P. Knappe and P. Wollan), preprint 2023; ArXiv
Tangle-tree duality: in graphs, matroids and beyond (with S. Oum), Combinatorica 39 (2019), 879-910; PDF.
Duality theorems for blocks and tangles in graphs (with J. Erde & Ph. Eberenz), SIDMA 31 (2017) 1514-1528, 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), 171-192; PDF
Unifying duality theorems for width parameters I. Weak and strong duality (with S. Oum), ArXic 2014; PDF.
Unifying duality theorems for width parameters II. General duality (with S. Oum), ArXiv 2014; PDF.
The Erdös-Pósa property for clique minors in highly connected graphs (with K. Kawarabayashi & P. Wollan), J. Combin. Theory (Series B) 102 (2012), 454-469; PDF.
On the excluded minor structure theorem for graphs of large tree-width (with K. Kawarabayashi, T. Müller & P. Wollan), J. Combin. Theory (Series B) 102 (2012), 1189-1210; PDF.
Graph minor hierarchies (with D. Kühn), Discrete Applied Mathematics 145 (2005), 167-182; abstract; PDF
Dense minors in graphs of large girth (with C. Rempel), Combinatorica 25 (2005), 111-116; abstract; PDF
Two short proofs concerning tree-decompositions (with P. Bellenbaum), Combinatoric, Probability and Computing 11 (2002), 1-7; 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), 61-73; 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), 27-30; 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, 223-244; PDF.
Forcing finite minors in sparse infinite graphs by large-degree assumptions, Electronic J. Comb. 22 (2015), #P1.43; PDF
A short proof of Halin's grid theorem, Abh. Math. Sem. Univ. Hamburg 74 (2004), 137-242; abstract; PDF
An accessibility theorem for infinite graph minors, J. Graph Theory 35 (2000), 273-277; abstract; DVI; PDF
Normal spanning trees, Aronszajn trees and excluded minors (with I. Leader), J. London Math. Soc. 63 (2001), 16-32; abstract; PDF
A universal planar graph under the minor relation (with D. Kühn), J. Graph Theory 32 (1999), 191-206; abstract; PDF
Excluding a countable clique (with R. Thomas), J. Combin. Theory (Series B) 76 (1999), 41-67; abstract; PDF
The depth-first search tree structure of TKomega-free graphs, J. Combin. Theory (Series B) 61 (1994), 260-262. DVI
The structure of TKa-free graphs, J. Combin. Theory (Series B) 54 (1992), 222-238. PDF
Simplicial minors and decompositions of graphs, Math. Proc. Camb. Phil. Soc. 103 (1988), 409-426. DVI
On universal graphs with forbidden topological subgraphs, Europ. J. Combinatorics 6 (1985), 175-182.
On the problem of finding small subdivision and homomorphism bases for classes of countable graphs, Discrete Mathematics 55 (1985), 21-33.

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) 32-53; PDF
On the homology of locally compact spaces with ends (with P. Sprüssel), Topology and its Applications 158 (2011), 1626-1639; 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), 681-714; abstract; PDF
End spaces and spanning trees, J. Combin. Theory (Series B) 96 (2006), 846-854; abstract; DVI; PDF
Duality in infinite graphs (with H. Bruhn), Comb. Probab. Computing 15 (2006), 75-90; abstract; PDF
Cycle-cocycle partitions and faithful cycle covers for locally finite graphs (with H. Bruhn & M. Stein), J. Graph Theory 50 (2005), 150-161; abstract; PDF
The cycle space of an infinite graph, Combinatorics, Probability and Computing 14 (2005), 59-79; abstract; PDF
Graph-theoretical versus topological ends of graphs (with D. Kühn), J. Combin. Theory (Series B) 87 (2003), 197-206; abstract; PDF
Topological paths, cycles and spanning trees in infinite graphs (with D. Kühn), Europ. J. Combinatorics 25 (2004), 835-862; abstract; PDF
On infinite cycles I (with D. Kühn), Combinatorica 24 (2004), 68-89; abstract; PDF
On infinite cycles II (with D. Kühn), Combinatorica 24 (2004), 91-116; abstract; PDF

Growth in infinite graphs

The classification of finitely spreading graphs, Proc. London Math. Soc (3) 73 (1996), 534-554. PDF
Dominating functions and graphs (with S. Shelah and J. Steprans), J. London Math. Soc 49 (1994) 16-24. DVI
The growth of infinite graphs (with I. Leader): boundedness and finite spreading, Combinatorics, Probability and Computing 3 (1994) 51-55. DVI; PDF
Dominating functions and topological graph minors, Contemporary Mathematics 147 (1993), 461-476. PDF
A proof of the Bounded Graph Conjecture (with I. Leader), Invent. math. 108 (1992), 131-162; 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), 846-854; abstract; DVI; PDF
Normal spanning trees, Aronszajn trees and excluded minors (with I. Leader), J. London Math. Soc 63 (2001), 16-32; abstract; PDF
Normal tree orders for infinite graphs (with J.M. Brochet), Trans. Amer. Math. Soc 345 (1995), 871-895. DVI
The depth-first search tree structure of TKomega-free graphs, J. Combin. Theory (Series B) 61 (1994), 260-262. 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) 32-53; PDF
Forcing finite minors in sparse infinite graphs by large-degree 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), 2643-2675; abstract; PDF.
The homology of locally finite graphs with ends (with P. Sprüssel), Combinatorica 30 (2010), 681-714; abstract; PDF.
End spaces and spanning trees, J. Combin. Theory (Series B) 96 (2006), 846-854; abstract; DVI; PDF
Menger's theorem for infinite graphs with ends (with H. Bruhn & M. Stein), J. Graph Theory 50 (2005), 199-211; abstract; DVI; PDF
A short proof of Halin's grid theorem, Abh. Math. Sem. Univ. Hamburg 74 (2004), 137-242; abstract; PDF
Duality in infinite graphs (with H. Bruhn), Combinatoric, Probability and Computing 15 (2006), 75-90; abstract; PDF
Cycle-cocycle partitions and faithful cycle covers for locally finite graphs (with H. Bruhn & M. Stein), J. Graph Theory 50 (2005), 150-161; abstract; PDF
The Erdös-Menger conjecture for source/sink sets with disjoint closures, J. Comb. Theory (Series B) 93 (2005), 107-114; abstract; DVI; PDF
The cycle space of an infinite graph, Combinatorics, Probability and Computing 14 (2005), 59-79; abstract; PDF
The countable Erdös-Menger conjecture with ends, J. Combin. Theory (Series B) 87 (2003), 145-161; abstract; PDF
Graph-theoretical versus topological ends of graphs (with D. Kühn), J. Combin. Theory (Series B) 87 (2003), 197-206; abstract; PDF
Topological paths, cycles and spanning trees in infinite graphs (with D. Kühn), Europ. J. Combinatorics 25 (2004), 835-862; abstract; PDF
On infinite cycles I (with D. Kühn), Combinatorica 24 (2004), 68-89; abstract; PDF
On infinite cycles II (with D. Kühn), Combinatorica 24 (2004), 91-116; abstract; PDF
Normal tree orders for infinite graphs (with J.M. Brochet), Trans. Amer. Math. Soc 345 (1995), 871-895. DVI
The depth-first search tree structure of TKomega-free graphs, J. Combin. Theory (Series B) 61 (1994), 260-262. DVI
On vertex transitive graphs of infinite degree (with H.A. Jung and R. Möller), Arch. Math. 60 (1993), 591-600. DVI
The end structure of a graph, Discrete Mathematics 100 (1992), 313-327. DVI
On spanning trees and k-connectedness in infinite graphs, J. Combin. Theory (Series B) 56 (1992), 263-277. DVI
On end-faithful spanning trees in infinite graphs, Math. Proc. Camb. Phil. Soc. 107 (1990), 461-473. PDF

Erdös-Menger conjecture; paths in infinite graphs

A Cantor-Bernstein theorem for paths in graphs (with C. Thomassen), Amer. Math. Monthly 113 (2006), 161-166; abstract; PDF
Menger's theorem for infinite graphs with ends (with H. Bruhn & M. Stein), J. Graph Theory 50 (2005), 199-211; abstract; DVI; PDF
The Erdös-Menger conjecture for source/sink sets with disjoint closures, J. Comb. Theory (Series B) 93 (2005), 107-114; abstract; DVI; PDF
The countable Erdös-Menger conjecture with ends, J. Combin. Theory (Series B) 87 (2003), 145-161; abstract; PDF
Menger's theorem for a countable source set (with R. Aharoni), Combinatorics, Probability and Computing 3 (1994), 145-156; DVI
A proof of the Erdös-Menger conjecture for countably connected graphs without large simplices, preprint 1988. DVI (subsumed in Graph Decompositions)

Algebraic graph theory

Homological aspects of oriented hypergraphs, ArXiv 2021; PDF
Profinite separation systems (with J. Kneip), Order 37 (2020), 179-205; short/long version
Structural submodularity and tangles in abstract separation systems (with J. Erde & D. Weißauer), JCTA 167C (2019), 155-180; PDF
Abstract separation systems, Order 35 (2018), 157-170; PDF
Tangle-tree duality: in graphs, matroids and beyond (with S. Oum), Combinatorica 39 (2019), 879-910; 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), 681-714; abstract; PDF
MacLane's theorem for arbitrary surfaces (with H. Bruhn), J. Combin. Theory (Series B) 99 (2009) 275-286; abstract; short; extended
Duality in infinite graphs (with H. Bruhn), Combinatoric, Probability and Computing 15 (2006), 75-90; abstract; PDF
The cycle space of an infinite graph, Combinatorics, Probability and Computing 14 (2005), 59-79; abstract; PDF
On infinite cycles I (with D. Kühn), Combinatorica 24 (2004), 68-89; abstract; PDF
On infinite cycles II (with D. Kühn), Combinatorica 24 (2004), 91-116; abstract; PDF
A conjecture concerning a limit of non-Cayley graphs (with I. Leader), J. Algebraic Combinatorics 14 (2001), 17-25; abstract; PDF
On vertex transitive graphs of infinite degree (with H.A. Jung and R. Möller), Arch. Math. 60 (1993), 591-600. DVI

Extremal graph theory

Global connectivity and expansion: long cycles and factors in f-connected graphs (with St. Brandt, H. Broersma, & M. Kriesell), Combinatorica 26 (2006), 17-36; abstract; PDF
Dense minors in graphs of large girth (with C. Rempel), Combinatorica 25 (2005), 111-116; abstract; PDF

Planar graphs and graphs in surfaces

MacLane's theorem for arbitrary surfaces (with H. Bruhn), J. Combin. Theory (Series B) 99 (2009) 275-286; abstract; short; extended
Duality in infinite graphs (with H. Bruhn), Comb. Probab. Computing 15 (2006), 75-90; abstract; PDF
A universal planar graph under the minor relation (with D. Kühn), J. Graph Theory 32 (1999), 191-206; abstract; PDF
Excluding a countable clique (with R. Thomas), J. Combin. Theory (Series B) 76 (1999), 41-67; abstract; PDF
A separation property of planar triangulations, J. Graph Theory 11 (1987), 43-52.55 (1985), 21-33.

Simplicial decompositions of graphs

Decomposing infinite graphs, Discrete Mathematics 95 (1991), 69-89. PDF (Expository introduction to Graph Decompositions)
A compactness theorem for complete separators, Abh. Math. Sem. Univ. Hamburg 60 (1990), 149-151. DVI
Simplicial minors and decompositions of graphs, Math. Proc. Camb. Phil. Soc. 103 (1988), 409-426. DVI
Simplicial tree-decompositions of infinite graphs I, J. Combin. Theory (Series B) 48 (1990), 197-215. DVI
Simplicial tree-decompositions of infinite graphs II - the existence of prime decompositions, J. Combin. Theory (Series B) 50 (1990), 93-116. DVI
Simplicial tree-decompositions of infinite graphs III - the uniqueness of prime decompositions, J. Combin. Theory (Series B) 50 (1990), 117-128. DVI
Simplicial decompositions of graphs - a survey of applications, Discrete Mathematics 75 (1989), 121-144. DVI
Simplicial decompositions, tree-decompositions and graph minors, Ars Combinatoria 25C (1988), 97-104. 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), 133-145.
A separation property of planar triangulations, J. Graph Theory 11 (1987), 43-52.

Universal graphs

A universal planar graph under the minor relation (with D. Kühn), J. Graph Theory 32 (1999), 191-206; abstract; PDF
Some remarks on universal graphs (with R. Halin and W. Vogler), Combinatorica 5 (1985), 283-293.
On the problem of finding small subdivision and homomorphism bases for classes of countable graphs, Discrete Mathematics 55 (1985), 21-33.
On universal graphs with forbidden topological subgraphs, Europ. J. Combinatorics 6 (1985), 175-182.

Matroids

Tangle-tree duality: in graphs, matroids and beyond (with S. Oum), Combinatorica 39 (2019), 879-910; PDF.
Profiles of separations: in graphs, matroids and beyond (with F. Hundertmark & S. Lemanczyk), Combinatorica 39 (2019), 37–75; PDF
The structure of 2-separations of infinite matroids (with E. Aigner-Horev & L. Postle), J. Combin. Theory (Series B) 116 (2016), 25-56; PDF
Infinite matroids in graphs (with H. Bruhn), in the Infinite Graph Theory special volume of Discrete Math 311 (2011), 1461-1471; PDF
Axioms for infinite matroids (with H. Bruhn, M. Kriesell, R. Pendavingh & P. Wollan), Adv. Math 239 (2013), 18-46; PDF

Infinite combinatorics, orders and logic

Profinite separation systems (with J. Kneip), Order 37 (2020), 179-205; short/long version
Tree sets, Order 35 (2018), 171-192; PDF
Twins of rayless graphs (with A. Bonato, H. Bruhn & P. Sprüssel), J. Combin. Theory (Series B) 101 (2011) 60-65; PDF.
Every rayless graph has an unfriendly partition (with H. Bruhn, A. Georgakopoulos & P. Sprüssel), Combinatorica 30 (2010), 521-532; DVI, PDF.
Orientations and partitions of the Rado graph (with I. Leader, A. Scott & St. Thomassé), Trans. Amer. Math. Soc 359 No.5 (2007), 2395-2405; abstract; DVI; PDF
A Cantor-Bernstein theorem for paths in graphs (with C. Thomassen), Amer. Math. Monthly 113 (2006), 161-166; abstract; PDF
On the cofinality of infinite partially ordered sets: factoring a poset into lean essential subsets (with O. Pikhurko), Order 20 (2003), 53--66; abstract; DVI; PDF
Relating subsets of a poset, and a partition theorem for WQOs, Order 18 (2001), 275--279; abstract; DVI; PDF
Normal spanning trees, Aronszajn trees and excluded minors (with I. Leader), J. London Math. Soc 63 (2001), 16--32; abstract; PDF
An accessibility theorem for infinite graph minors, J. Graph Theory 35 (2000), 273-277; abstract DVI; PDF
Normal tree orders for infinite graphs (with J.M. Brochet), Trans. Amer. Math. Soc 345 (1995), 871-895; DVI
Domination games on infinite graphs (with I. Leader), Theor. Computer Science A 132 (1994), 337-345; PDF
Dominating functions and graphs (with S. Shelah and J. Steprans), J. London Math. Soc 49 (1994) 16-24; DVI

Topology

Canonical graph decompositions via coverings (with R. Jacobs, P. Knappe and J. Kurkofka), preprint 2022; ArXiv
Homological aspects of oriented hypergraphs, ArXiv 2021; PDF
Ends and tangles, Abhandlungen Math. Sem. Univ. Hamburg 87 (2017), Special volume in memory of Rudolf Halin, 223-244; PDF
On the homology of locally compact spaces with ends (with P. Sprüssel), Topology and its Applications 158 (2011), 1626-1639; PDF
The fundamental group of a locally finite graph with ends (with P. Sprüssel), Adv. Math 226 (2011), 2643-2675; abstract; PDF.
The homology of locally finite graphs with ends (with P. Sprüssel), Combinatorica 30 (2010), 681-714; abstract; PDF.

Applications outside mathematics

Traits and tangles: an analysis of the Big Five paradigm by tangle-based clustering (with H. v.Bergen), preprint 2024, PDF
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 (pre-1995) cases I managed to produce PDF files with partial figures, which are also posted above.

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