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 Robin R Thomas

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Average citations per article13.64
Citation Count955
Publication count70
Publication years1990-2016
Available for download8
Average downloads per article462.75
Downloads (cumulative)3,702
Downloads (12 Months)147
Downloads (6 Weeks)21
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70 results found Export Results: bibtexendnoteacmrefcsv

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1
November 2016 Journal of Combinatorial Theory Series B: Volume 121 Issue C, November 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

Almost 4-connectivity is a weakening of 4-connectivity which allows for vertices of degree three. In this paper we prove the following theorem. Let G be an almost 4-connected triangle-free planar graph, and let H be an almost 4-connected non-planar graph such that H has a subgraph isomorphic to a subdivision ...
Keywords: Graph, Subdivision, Planarity, Non-planar extension

2
July 2016 Journal of Combinatorial Theory Series B: Volume 119 Issue C, July 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

A graph is apex if there is a vertex whose deletion makes the graph planar, and doublecross if it can be drawn in the plane with only two crossings, both incident with the infinite region in the natural sense. In 1966, Tutte 9 conjectured that every two-edge-connected cubic graph with ...
Keywords: Edge-colouring, Four-colour theorem, Petersen minor

3
July 2016 Journal of Combinatorial Theory Series B: Volume 119 Issue C, July 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

Let G be a plane graph with outer cycle C and let ( L ( v ) : v � V ( G ) ) be a family of sets such that | L ( v ) | � 5 for every v � V ( G ) . By ...
Keywords: 5-list-coloring, Critical graph, Planar graph

4
May 2016 Journal of Combinatorial Theory Series B: Volume 118 Issue C, May 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

We prove that every internally 4-connected non-planar bipartite graph has an odd K 3 , 3 subdivision; that is, a subgraph obtained from K 3 , 3 by replacing its edges by internally disjoint odd paths with the same ends. The proof gives rise to a polynomial-time algorithm to find ...
Keywords: Pfaffian orientation, Bipartite graph, Odd K 3 , 3 subdivision

5
March 2015 Journal of Combinatorial Theory Series B: Volume 111 Issue C, March 2015
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 1

Let G be a plane graph with outer cycle C, let v 1 , v 2 � V ( C ) and let ( L ( v ) : v � V ( G ) ) be a family of sets such that | L ( v 1 ) | ...
Keywords: Choosability, Graph, List-coloring, Planar graph

6
November 2013 Journal of Combinatorial Theory Series B: Volume 103 Issue 6, November, 2013
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^n^^^1^^^/^^^1^^^2^/^2^0^0^0^0 distinct 3-colorings. We show that it has at least 2^n^/^2^1^2 distinct 3-colorings.
Keywords: Coloring, Triangle-free planar graph, Graph

7 published by ACM
October 2013 Journal of the ACM (JACM): Volume 60 Issue 5, October 2013
Publisher: ACM
Bibliometrics:
Citation Count: 4
Downloads (6 Weeks): 5,   Downloads (12 Months): 22,   Downloads (Overall): 210

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We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nešetřil and Ossona de Mendez. This generalizes several results from the literature, because many natural classes of graphs have bounded expansion: graphs of bounded tree-width, all proper minor-closed ...
Keywords: graphs with bounded expansion, tree-depth, First-order model checking

8
September 2012 Journal of Combinatorial Theory Series B: Volume 102 Issue 5, September, 2012
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 1

We exhibit an explicit list of nine graphs such that a graph drawn in the Klein bottle is 5-colorable if and only if it has no subgraph isomorphic to a member of the list.
Keywords: Graph, Klein bottle, Coloring

9
January 2012 Journal of Combinatorial Theory Series B: Volume 102 Issue 1, January, 2012
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 1

We show that every sufficiently large plane triangulation has a large collection of nested cycles that either are pairwise disjoint, or pairwise intersect in exactly one vertex, or pairwise intersect in exactly two vertices. We apply this result to show that for each fixed positive integer k, there are only ...
Keywords: Crossing numbers, Nested cycles, Crossing-critical, Triangulations

10
November 2011 Combinatorica: Volume 31 Issue 4, November 2011
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 1

We give an “excluded minor” and a “structural” characterization of digraphs D that have the property that for every subdigraph H of D , the maximum number of disjoint circuits in H is equal to the minimum cardinality of a set T ⊆ V ( H ) such that H\T ...
Keywords: 90C47

11 published by ACM
September 2011 ACM Transactions on Algorithms (TALG): Volume 7 Issue 4, September 2011
Publisher: ACM
Bibliometrics:
Citation Count: 3
Downloads (6 Weeks): 3,   Downloads (12 Months): 27,   Downloads (Overall): 425

Full text available: PDFPDF
Grötzsch's theorem states that every triangle-free planar graph is 3-colorable, and several relatively simple proofs of this fact were provided by Thomassen and other authors. It is easy to convert these proofs into quadratic-time algorithms to find a 3-coloring, but it is not clear how to find such a coloring ...
Keywords: Graph coloring, triangle-free graphs, planar graphs

12
March 2011 Journal of Combinatorial Theory Series B: Volume 101 Issue 2, March, 2011
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 3

We prove that, for every positive integer k, there is an integer N such that every 4-connected non-planar graph with at least N vertices has a minor isomorphic to K"4","k, the graph obtained from a cycle of length 2k+1 by adding an edge joining every pair of vertices at distance ...
Keywords: Crossing number, Crossing-critical, Minor, Non-planar graph, Subdivision

13
May 2010 Journal of Combinatorial Theory Series B: Volume 100 Issue 3, May, 2010
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 3

All K"4-free graphs with no odd hole and no odd antihole are three-colourable, but what about K"4-free graphs with no odd hole? They are not necessarily three-colourable, but we prove a conjecture of Ding that they are all four-colourable. This is a consequence of a decomposition theorem for such graphs; ...
Keywords: Odd hole, Perfect graph

14
November 2009 Combinatorial Algorithms: 20th International Workshop, IWOCA 2009, Hradec nad Moravicí, Czech Republic, June 28---July 2, 2009, Revised Selected Papers
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 0

A graph G has a K t minor if a graph isomorphic to K t , the complete graph on t vertices, can be obtained from a subgraph of G by contracting edges. A long-standing conjecture of Hadwiger states that every graph with no K t minor is ( t ...

15
January 2009 SODA '09: Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 6
Downloads (6 Weeks): 0,   Downloads (12 Months): 6,   Downloads (Overall): 195

Full text available: PDFPDF
Grötzsch's theorem states that every triangle-free planar graph is 3-colorable, and several relatively simple proofs of this fact were provided by Thomassen and other authors. It is easy to convert these proofs into quadratic-time algorithms to find a 3-coloring, but it is not clear how to find such a coloring ...

16
January 2009 SODA '09: Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 9
Downloads (6 Weeks): 0,   Downloads (12 Months): 10,   Downloads (Overall): 195

Full text available: PDFPDF
Gimbel and Thomassen asked whether 3-colorability of a triangle-free graph drawn on a fixed surface can be tested in polynomial time. We settle the question by giving a linear-time algorithm for every surface which combined with previous results gives a lineartime algorithm to compute the chromatic number of such graphs. ...

17
September 2008 Journal of Combinatorial Theory Series B: Volume 98 Issue 5, September, 2008
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 2

A graph is k-linked if for every set of 2k distinct vertices {s"1,...,s"k,t"1,...,t"k} there exist disjoint paths P"1,...,P"k such that the endpoints of P"i are s"i and t"i. We prove every 6-connected graph on n vertices with 5n-14 edges is 3-linked. This is optimal, in that there exist 6-connected graphs ...
Keywords: Disjoint paths, Graph, Connectivity, Graph linkages

18
September 2008 Journal of Combinatorial Theory Series B: Volume 98 Issue 5, September, 2008
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 4

We consider the question of characterizing Pfaffian graphs. We exhibit an infinite family of non-Pfaffian graphs minimal with respect to the matching minor relation. This is in sharp contrast with the bipartite case, as Little [C.H.C. Little, A characterization of convertible (0,1)-matrices, J. Combin. Theory Ser. B 18 (1975) 187-208] ...
Keywords: Perfect matching, Graph, Pfaffian orientation, Factor-critical graph

19
May 2008 Combinatorica: Volume 28 Issue 3, May 2008
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 1

We prove that a triangle-free graph drawn in the torus with all faces bounded by even walks is 3-colorable if and only if it has no subgraph isomorphic to the Cayley graph C ( Z 13 ; 1,5). We also prove that a non-bipartite quadrangulation of the Klein bottle is ...
Keywords: 05C10

20
January 2008 Combinatorica: Volume 28 Issue 1, January 2008
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

We relate signs of edge-colorings (as in classical Penrose's result) with "Pfaffian labelings", a generalization of Pfaffian orientations, whereby edges are labeled by elements of an Abelian group with an element of order two. In particular, we prove a conjecture of Goddyn that all k -edge-colorings of a k -regular ...
Keywords: 05C10, 05C70, 05C75, 05C15



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