Sum-perfect graphs

Inspired by a famous characterization of perfect graphs due to Lov\'{a}sz, we define a graph \(G\) to be sum-perfect if for every induced subgraph \(H\) of \(G\), \(\alpha(H) + \omega(H) \geq |V(H)|\). (Here \(\alpha\) and \(\omega\) denote the stability number and clique number, respectively.)...

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Bibliographic Details
Published inarXiv.org
Main Authors Litjens, Bart, Polak, Sven, Sivaraman, Vaidy
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.10.2017
Subjects
Graph theory
Graphs
Mathematics - Combinatorics
Online AccessGet full text
ISSN2331-8422
DOI10.48550/arxiv.1710.07546

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Summary:Inspired by a famous characterization of perfect graphs due to Lov\'{a}sz, we define a graph \(G\) to be sum-perfect if for every induced subgraph \(H\) of \(G\), \(\alpha(H) + \omega(H) \geq |V(H)|\). (Here \(\alpha\) and \(\omega\) 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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1710.07546