On the Existence of Critical Clique-Helly Graphs

A graph is clique-Helly if any family of mutually intersecting cliques has non-empty intersection. Dourado, Protti and Szwarcfiter conjectured that every clique-Helly graph contains a vertex whose removal maintains it a clique-Helly graph. We will present a counterexample to this conjecture.

Detalhes bibliográficos
Autores: Alcón, Liliana Graciela, Pizaña, Miguel, Ravenna, Gabriela Susana
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2017
País:Argentina
Recursos:Universidad Nacional de La Plata
Repositório:SEDICI (UNLP)
Idioma:inglês
OAI Identifier:oai:sedici.unlp.edu.ar:10915/102977
Acesso em linha:http://sedici.unlp.edu.ar/handle/10915/102977
Access Level:Acceso aberto
Palavra-chave:Matemática
Helly property
Clique-Helly graphs
Clique graphs
Descrição
Resumo:A graph is clique-Helly if any family of mutually intersecting cliques has non-empty intersection. Dourado, Protti and Szwarcfiter conjectured that every clique-Helly graph contains a vertex whose removal maintains it a clique-Helly graph. We will present a counterexample to this conjecture.