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On the tree-width of even-hole-free graphs [article]

Pierre Aboulker, Isolde Adler, Eun Jung Kim, Ni Luh Dewi Sintiari, Nicolas Trotignon
2020 arXiv   pre-print
We prove the conjecture for subcubic graphs and we give a bound on the tree-width of the class of (even hole, pyramid)-free graphs of degree at most 4.  ...  The class of all even-hole-free graphs has unbounded tree-width, as it contains all complete graphs.  ...  The class of all even-hole-free graphs trivially has unbounded tree-width, as is contains all complete graphs.  ... 
arXiv:2008.05504v1 fatcat:ij2smflzl5dx5h6sladobes5ve

On rank-width of even-hole-free graphs [article]

Isolde Adler, Ngoc Khang Le, Haiko Müller, Marko Radovanović, Nicolas Trotignon, Kristina Vušković
2017 arXiv   pre-print
We present a class of (diamond, even hole)-free graphs with no clique cutset that has unbounded rank-width.  ...  In general, even-hole-free graphs have unbounded rank-width, because chordal graphs are even-hole-free. A.A. da Silva, A. Silva and C.  ...  Rank-width of subclasses of even-hole-free graphs has also been studied. In [12] it is shown that planar even-hole-free graphs have tree-width at most 49.  ... 
arXiv:1611.09907v2 fatcat:hgtsktipz5gytac7dkcjlz62le

Coloring even-hole-free graphs with no star cutset [article]

Ngoc Khang Le
2018 arXiv   pre-print
In this paper, we study the class of even-hole-free graphs with no star cutset.  ...  A hole is a chordless cycle of length at least 4. A graph is even-hole-free if it does not contain any hole of even length as an induced subgraph.  ...  The rank-width of a clique is at most 1 and the rank-width of a hole is at most 2. 3 χ-bounding function 3 .1 Special graphs Recall that the bound of chromatic number for even-hole-free graphs (χ(G)  ... 
arXiv:1805.01948v1 fatcat:ro44af5s6zaetefh4ewn37qqju

On the structure of (pan, even hole)-free graphs [article]

Kathie Cameron, Steven Chaplick, Chinh T. Hoang
2017 arXiv   pre-print
Using this structure theorem, we show that the tree-width of a (pan, even hole)-free graph is at most 1.5 times the clique number minus 1, and thus the chromatic number is at most 1.5 times the clique  ...  A hole is a chordless cycle with at least four vertices. A pan is a graph which consists of a hole and a single vertex with precisely one neighbor on the hole.  ...  Problem 7.2 Is the tree-width of an even-hole-free graph bounded by a function of its clique number?  ... 
arXiv:1508.03062v2 fatcat:futyzwrk6zhp3gxxtreiof2cti

Structure and algorithms for (cap, even hole)-free graphs [article]

Kathie Cameron, Murilo V. G. da Silva, Shenwei Huang, Kristina Vušković
2016 arXiv   pre-print
A graph is even-hole-free if it has no induced even cycles of length 4 or more. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle.  ...  In this paper, we consider (cap, even hole)-free graphs, and more generally, (cap, 4-hole)-free odd-signable graphs. We give an explicit construction of these graphs.  ...  We would like to thank Haiko Müller for fruitful discussions, and to thank Jerry Spinrad for pointing to us the idea of finding true twins in O(n + m) time.  ... 
arXiv:1611.08066v1 fatcat:we3h6o6bofeldlbzy6ouyaux6y

Structure and algorithms for (cap, even hole)-free graphs

Kathie Cameron, Murilo V.G. da Silva, Shenwei Huang, Kristina Vušković
2018 Discrete Mathematics  
Abstract A graph is even-hole-free if it has no induced even cycles of length 4 or more. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle.  ...  In this paper, we consider (cap, even hole)-free graphs, and more generally, (cap, 4-hole)-free odd-signable graphs. We give an explicit construction of these graphs.  ...  We would like to thank Haiko Müller for fruitful discussions, and to thank Jerry Spinrad for pointing to us the idea of finding true twins in O(n + m) time.  ... 
doi:10.1016/j.disc.2017.09.013 fatcat:lrcmtmfz4rg5hd6iikquqhpnny

Page 779 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
David Burns (1-FERR; Big Rapids, MI) 2001b:05189 05C75 Kotlov, Andrei (3-WTRL-B; Waterloo, ON) Spectral characterization of tree-width-two graphs.  ...  A subset of edges in a signed graph is odd [even] if it contains an odd [even] number of odd labeled edges. A hole in a graph is a chordless cycle containing at least four edges.  ... 

Transformations of representation in constraint satisfaction

András Z. Salamon
2015 Constraints  
My main contribution is an investigation of such hybrid CSPs which cannot be defined with either one of these kinds of restrictions.  ...  graphs for which an independent set of specified size can be found efficiently.  ...  Since MS(Tree) is hereditary, it is therefore the class of (X, odd-hole, antihole)-free graphs, for some set X of graphs.  ... 
doi:10.1007/s10601-015-9224-8 fatcat:lollakqzx5h7xeajtfrmaz6u4q

From χ- to χ_p-bounded classes [article]

Y. Jiang, J. Nesetril, P. Ossona de Mendez
2021 arXiv   pre-print
As an application of our characterizations, among other things, we show that for every odd integer g>3 even hole-free graphs G contain at most φ(g,ω(G)) |G| holes of length g.  ...  On the way, we generalize a result of Wood relating the chromatic number of a graph to the star chromatic number of its 1-subdivision.  ...  Acknowledgements The authors would like to thank the anonymous referees for his corrections and suggestions.  ... 
arXiv:2009.02953v2 fatcat:woph6rwtvbdg7p3yjp5xxnsodq

(Theta, triangle)-free and (even hole, K_4)-free graphs. Part 1 : Layered wheels [article]

Ni Luh Dewi Sintiari, Nicolas Trotignon
2021 arXiv   pre-print
They also provide examples of graphs of large treewidth and large rankwidth in well-studied classes, such as (theta, triangle)-free graphs and even-hole-free graphs with no K_4 (where a hole is a chordless  ...  cycle of length at least four, a theta is a graph made of three internally vertex disjoint paths of length at least two linking two vertices, and K_4 is the complete graph on four vertices).  ...  Even-hole-free graphs Our last motivation for this work is a better understanding of even-hole-free graphs.  ... 
arXiv:1906.10998v5 fatcat:fet7nsotbzcvflkd7huybdfomm

The independent set problem is FPT for even-hole-free graphs [article]

Edin Husic, Stephan Thomasse, Nicolas Trotignon
2019 arXiv   pre-print
The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem.  ...  Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs.  ...  Closely related to the class of perfect graphs is the class of even-hole-free graphs. The class of even-hole-free graphs was introduced as a class structurally similar to the class of Berge graphs.  ... 
arXiv:1907.01083v2 fatcat:ot4sjpepsfejhc37eskw7dfcii

The Independent Set Problem Is FPT for Even-Hole-Free Graphs

Edin Husic, Stéphan Thomassé, Nicolas Trotignon, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem.  ...  Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs.  ...  Lemma 8 shows that the bi-trees arising from even-hole-free graphs do not have the obstructions.  ... 
doi:10.4230/lipics.ipec.2019.21 dblp:conf/iwpec/HusicTT19 fatcat:pysgvpgbofbpxcst25u7kh2rby

A note on module-composed graphs [article]

Frank Gurski
2007 arXiv   pre-print
In this paper we consider module-composed graphs, i.e. graphs which can be defined by a sequence of one-vertex insertions v_1,...  ...  ,v_n, such that the neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of the graph defined by vertices v_1,..., v_i-1.  ...  Examples for distance hereditary graphs are co-graphs and trees. For the case of bipartite graphs 8 , the notion module-composed even is equivalent to the notion of distance hereditary. 1.  ... 
arXiv:0705.1521v2 fatcat:sid2wof7znhcnlhdj7lk35zrfy

Special tree-width and the verification of monadic second-order graph pr operties

Bruno Courcelle, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width.  ...  We introduce special tree-width, a graph complexity measure between path-width and tree-width. The corresponding automata are easier to construct than those for tree-width.  ...  It appears that the corresponding automata, even for the basic property of adjacency, have exponential size in the bound on tree-width.  ... 
doi:10.4230/lipics.fsttcs.2010.13 dblp:conf/fsttcs/Courcelle10 fatcat:msbselcwwrbcxkeg6k7cykki5y

Surfaces, Tree-Width, Clique-Minors, and Partitions

Guoli Ding, Bogdan Oporowski, Daniel P. Sanders, Dirk Vertigan
2000 Journal of combinatorial theory. Series B (Print)  
In 1971, Chartrand, Geller, and Hedetniemi conjectured that the edge set of a planar graph may be partitioned into two subsets, each of which induces an outerplanar graph.  ...  One such result, in which a planar graph may be thus edge partitioned into two series-parallel graphs, has nice generalizations for graphs embedded onto an arbitrary surface and graphs with no large clique-minor  ...  The tree-width of a graph G, in symbols tw(G), is the minimum integer k such that G is a partial k-tree. Another important class of graphs are graphs embeddable on a given surface.  ... 
doi:10.1006/jctb.2000.1962 fatcat:j7hw2spwajeaparmwn4uo4voae
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