Sum-perfect graphs

Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)≥|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is s...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 259; pp. 232 - 239
Main Authors Litjens, Bart, Polak, Sven, Sivaraman, Vaidy
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 30.04.2019
Elsevier BV
Subjects
Clique
Forbidden induced subgraph
Graph theory
Graphs
Perfect graph
Stable set
Sum-perfect graph
Forbidden induced subgraph
Clique
Stable set
Sum-perfect graph
Perfect graph
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2018.12.015

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Summary:Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)≥|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is sum-perfect if and only if G does not contain any of the graphs in the set as an induced subgraph.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.12.015