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A Description of Claw-Free Perfect Graphs
1999
Journal of combinatorial theory. Series B (Print)
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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]
2016
arXiv
pre-print
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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
2003
Discrete Applied Mathematics
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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
2004
Mathematical Methods of Operations Research
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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
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(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
2004
Discrete Mathematics
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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
2005
Electronic Notes in Discrete Mathematics
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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
2016
Mathematical programming
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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]
2014
arXiv
pre-print
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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
2010
Algorithmica
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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]
2010
Lecture Notes in Computer Science
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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
2012
Discrete Mathematics
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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
2001
Journal of combinatorial theory. Series B (Print)
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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]
2012
Lecture Notes in Computer Science
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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]
2020
arXiv
pre-print
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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
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