Filters








1,515 Hits in 2.3 sec

A Description of Claw-Free Perfect Graphs

Frédéric Maffray, Bruce A. Reed
1999 Journal of combinatorial theory. Series B (Print)  
This yields a complete description of the structure of claw-free Berge graphs and a new proof of their perfectness.  ...  It is known that all claw-free perfect graphs can be decomposed via clique-cutsets into two types of indecomposable graphs respectively called elementary and peculiar (1988, V. Chva tal and N.  ...  Every Claw-Free Berge Graph Is Perfect (New Proof ) The description of elementary graphs allows us to find a new and simple proof of the fact that they are perfect.  ... 
doi:10.1006/jctb.1998.1872 fatcat:sgjfbjus25e2hh6iyzu32w52ha

Lovász-Schrijver PSD-operator on Claw-Free Graphs [article]

Silvia Bianchi, Mariana Escalante, Graciela Nasini, Annegret Wagler
2016 arXiv   pre-print
An according conjecture has been recently formulated (_+-Perfect Graph Conjecture); here we verify it for the well-studied class of claw-free graphs.  ...  In particular, we look for a polyhedral relaxation of (G) that coincides with _+((G)) and (G) if and only if G is _+-perfect.  ...  First of all, we can determine the subclass of joined a-perfect graphs to which all LS + -perfect claw-free graphs belong to.  ... 
arXiv:1612.02670v1 fatcat:o6xiebog4jdxndzeyk63oaait4

Clique family inequalities for the stable set polytope of quasi-line graphs

G. Oriolo
2003 Discrete Applied Mathematics  
Quasi-line graphs are a subclass of claw-free graphs, and as for claw-free graphs, there exists a polynomial algorithm for finding a maximum weighted stable set on such graphs, but we do not have a complete  ...  In one of fundamental work in combinatorial optimization Edmonds gave a complete linear description of the matching polytope. Matchings in a graph are equivalent to stable sets its line graph.  ...  Observe that a graph is quasi-line and perfect if and only if it is claw-free and perfect.  ... 
doi:10.1016/s0166-218x(03)00400-1 fatcat:vai3up33sngjtot2itdwfyzt5y

On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs

Thomas M. Liebling, Gianpaolo Oriolo, Bianca Spille, Gautier Stauffer
2004 Mathematical Methods of Operations Research  
We deal with non-rank facets of the stable set polytope of claw-free graphs.  ...  Last but not least, we present a complete description of the stable set polytope for graphs with stability number 2, already observed by Cook [3] and Shepherd [18] .  ...  The authors gratefully acknowledge the support of DONET for this research.  ... 
doi:10.1007/s001860300317 fatcat:nb52aomjf5difa22wul3zdwu4q

Page 923 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
(F-PARIS6-CM; Paris) A description of claw-free perfect graphs. (English summary) J. Combin. Theory Ser. B 75 (1999), no. 1, 134-156.  ...  This description of claw-free perfect graphs together with Chvatal and Sbihi’s decom- position will yield a new proof of the result of Parthasarathy and Ravindra. G.  ... 

On the choice number of claw-free perfect graphs

Sylvain Gravier, Frédéric Maffray
2004 Discrete Mathematics  
We prove that every 3-chromatic claw-free perfect graph is 3-choosable.  ...  Claw-free perfect graphs We will be inspired by a decomposition of claw-free perfect graphs that was found by Chvà atal and Sbihi [1] .  ...  Every claw-free perfect graph G with (G) 6 3 satisÿes Ch(G) = (G). The proof of Theorem 1 is based on a decomposition for claw-free perfect graphs, which we present in Section 2.  ... 
doi:10.1016/s0012-365x(03)00292-9 fatcat:zmechdk2fnbuxfgqkuqrmrxlvu

Partial characterizations of clique-perfect graphs

Flavia Bonomo, Maria Chudnovsky, Guillermo Durán
2005 Electronic Notes in Discrete Mathematics  
A graph G is clique-perfect if the sizes of a minimum clique-transversal and a maximum clique-independent set are equal for every induced subgraph of G.  ...  The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known.  ...  a recent structure theorem for claw-free graphs [9] , that states that every claw-free graph can be built from a few basic classes by gluing them together in prescribed ways.  ... 
doi:10.1016/j.endm.2005.05.014 fatcat:3kfyi76ifrcxllli3c74cwfrhq

Integer round-up property for the chromatic number of some h-perfect graphs

Yohann Benchetrit
2016 Mathematical programming  
Our results imply the existence of a polynomial-time algorithm which computes the weighted chromatic number of t-perfect claw-free graphs and h-perfect line-graphs.  ...  These graphs form another proper subclass of claw-free graphs.  ...  These graphs appear in the context of the problem of finding a nice description of the stable set polytope of claw-free graphs.  ... 
doi:10.1007/s10107-016-1085-4 fatcat:5acj7pbi2vcbdhx7mguw6xzmgm

Integer round-up property for the chromatic number of some h-perfect graphs [article]

Yohann Benchetrit
2014 arXiv   pre-print
Our results imply the existence of a polynomial-time algorithm which computes the weighted chromatic number of t-perfect claw-free graphs and h-perfect line-graphs.  ...  We prove that every h-perfect line-graph and every t-perfect claw-free graph G has the integer round-up property for the chromatic number: for every non-negative integer weight c on the vertices of G,  ...  These graphs appear in the context of the problem of finding a nice description of the stable set polytope of claw-free graphs.  ... 
arXiv:1406.0757v1 fatcat:uvwsnazud5hzbkfnber4nvriru

Finding Induced Paths of Given Parity in Claw-Free Graphs

Pim van 't Hof, Marcin Kamiński, Daniël Paulusma
2010 Algorithmica  
Finally, we show that a shortest induced path of given parity between two specified vertices of a claw-free perfect graph can be found in O(n 7 ) time. An extended abstract of this paper has been  ...  Our results imply that the problem of deciding if two specified vertices of a claw-free graph form an even pair, as well as the problem of deciding if a given claw-free graph has an even pair, can be solved  ...  vertices in a claw-free perfect graph.  ... 
doi:10.1007/s00453-010-9470-5 fatcat:emwqsmiedbfrnc4qd35kei5xki

Finding Induced Paths of Given Parity in Claw-Free Graphs [chapter]

Pim van 't Hof, Marcin Kamiński, Daniël Paulusma
2010 Lecture Notes in Computer Science  
Finally, we show that a shortest induced path of given parity between two specified vertices of a claw-free perfect graph can be found in O(n 7 ) time. An extended abstract of this paper has been  ...  Our results imply that the problem of deciding if two specified vertices of a claw-free graph form an even pair, as well as the problem of deciding if a given claw-free graph has an even pair, can be solved  ...  vertices in a claw-free perfect graph.  ... 
doi:10.1007/978-3-642-11409-0_30 fatcat:hstidpzhcjgvzka2vl6sd6yxma

A characterization of claw-free b-perfect graphs

T. Karthick, Frédéric Maffray
2012 Discrete Mathematics  
Here we characterize the class of claw-free b-perfect graphs by giving a complete description of their structure.  ...  We characterize the class of claw-free b-perfect graphs by giving a complete description of their structure. All our graphs are simple, finite and undirected.  ...  See [5] for a survey of results in claw-free graphs. The structure of claw-free perfect graphs was described in [15] .  ... 
doi:10.1016/j.disc.2011.09.029 fatcat:5vfnvvvz4rapbnfkrhan6y3xiu

A Transformation Which Preserves the Clique Number

Michael U. Gerber, Alain Hertz
2001 Journal of combinatorial theory. Series B (Print)  
One of these two classes strictly contains claw-free graphs. Elsevier Science  ...  Using this transformation we derive a polynomial algorithm for the computation of the clique number of all graphs in a class which strictly contains diamond-free graphs.  ...  In the following, we prove the validity of the Strong Perfect Graph Conjecture for a class of graphs that strictly contains claw-free graphs. Consider the three graphs depicted in Fig. 4 .  ... 
doi:10.1006/jctb.2001.2061 fatcat:j4lj62hisrconfbitaajxm6roa

Minimum Weighted Clique Cover on Strip-Composed Perfect Graphs [chapter]

Flavia Bonomo, Gianpaolo Oriolo, Claudia Snels
2012 Lecture Notes in Computer Science  
We also design a new, more efficient, combinatorial algorithm for the mwcc problem on strip-composed claw-free perfect graphs.  ...  In this paper, we show that a mwcc of a perfect strip-composed graph, with the basic graphs belonging to a class G, can be found in polynomial time, provided that the mwcc problem can be solved on G in  ...  Application to strip-composed claw-free perfect graphsAs an application of Theorem 2, we give a new algorithm for the mwcc on stripcomposed claw-free perfect graphs.  ... 
doi:10.1007/978-3-642-34611-8_6 fatcat:bhtkybrokvbsvb2fkiw7qk55qy

Counting weighted independent sets beyond the permanent [article]

Martin Dyer, Mark Jerrum, Haiko Muller, Kristina Vuskovic
2020 arXiv   pre-print
Line graphs of bipartite graphs are perfect graphs, and are known to be precisely the class of (claw, diamond, odd hole)-free graphs. So how far does the result of Jerrum, Sinclair and Vigoda extend?  ...  We first show that it extends to (claw, odd hole)-free graphs, and then show that it extends to the even larger class of (fork, odd hole)-free graphs.  ...  Chvátal and Sbihi [10] investigated the structure of claw-free perfect graphs as a special class of perfect graphs. These are closely related to (claw, odd hole)-free graphs.  ... 
arXiv:1909.03414v2 fatcat:5kzdr24yg5eplc2cfb4dvfati4
« Previous Showing results 1 — 15 out of 1,515 results