On the homotopy type of the clique graph

Detalhes bibliográficos
Autor(a) principal: Larrión,F.
Data de Publicação: 2001
Outros Autores: Neumann-Lara,V., Pizaña,M. A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Journal of the Brazilian Computer Society
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002001000200010
Resumo: If G is a graph, its clique graph K(G) is the intersection graph of all its (maximal) cliques. The complex G<FONT FACE=Symbol>­</FONT> of a graph G is the simplicial complex whose simplexes are the vertex sets of the complete subgraphs of G. Here we study a sufficient condition for G<FONT FACE=Symbol>­</FONT> and K(G)<FONT FACE=Symbol>­</FONT> to be homotopic. Applying this result to Whitney triangulations of surfaces, we construct an infinite family of examples which solve in the affirmative Prisner's open problem 1 in Graph Dynamics (Longman, Harlow, 1995): Are there finite connected graphs G that are periodic under K and where the second modulo 2 Betti number is greater than 0?
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spelling On the homotopy type of the clique graphclique graphsclique convergenceWhitney triangulationsclean triangulationssimplicial complexesmodulo 2 Betti numbersIf G is a graph, its clique graph K(G) is the intersection graph of all its (maximal) cliques. The complex G<FONT FACE=Symbol>­</FONT> of a graph G is the simplicial complex whose simplexes are the vertex sets of the complete subgraphs of G. Here we study a sufficient condition for G<FONT FACE=Symbol>­</FONT> and K(G)<FONT FACE=Symbol>­</FONT> to be homotopic. Applying this result to Whitney triangulations of surfaces, we construct an infinite family of examples which solve in the affirmative Prisner's open problem 1 in Graph Dynamics (Longman, Harlow, 1995): Are there finite connected graphs G that are periodic under K and where the second modulo 2 Betti number is greater than 0?Sociedade Brasileira de Computação2001-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002001000200010Journal of the Brazilian Computer Society v.7 n.3 2001reponame:Journal of the Brazilian Computer Societyinstname:Sociedade Brasileira de Computação (SBC)instacron:UFRGS10.1590/S0104-65002001000200010info:eu-repo/semantics/openAccessLarrión,F.Neumann-Lara,V.Pizaña,M. A.eng2003-12-16T00:00:00Zoai:scielo:S0104-65002001000200010Revistahttps://journal-bcs.springeropen.com/PUBhttps://old.scielo.br/oai/scielo-oai.phpjbcs@icmc.sc.usp.br1678-48040104-6500opendoar:2003-12-16T00:00Journal of the Brazilian Computer Society - Sociedade Brasileira de Computação (SBC)false
dc.title.none.fl_str_mv On the homotopy type of the clique graph
title On the homotopy type of the clique graph
spellingShingle On the homotopy type of the clique graph
Larrión,F.
clique graphs
clique convergence
Whitney triangulations
clean triangulations
simplicial complexes
modulo 2 Betti numbers
title_short On the homotopy type of the clique graph
title_full On the homotopy type of the clique graph
title_fullStr On the homotopy type of the clique graph
title_full_unstemmed On the homotopy type of the clique graph
title_sort On the homotopy type of the clique graph
author Larrión,F.
author_facet Larrión,F.
Neumann-Lara,V.
Pizaña,M. A.
author_role author
author2 Neumann-Lara,V.
Pizaña,M. A.
author2_role author
author
dc.contributor.author.fl_str_mv Larrión,F.
Neumann-Lara,V.
Pizaña,M. A.
dc.subject.por.fl_str_mv clique graphs
clique convergence
Whitney triangulations
clean triangulations
simplicial complexes
modulo 2 Betti numbers
topic clique graphs
clique convergence
Whitney triangulations
clean triangulations
simplicial complexes
modulo 2 Betti numbers
description If G is a graph, its clique graph K(G) is the intersection graph of all its (maximal) cliques. The complex G<FONT FACE=Symbol>­</FONT> of a graph G is the simplicial complex whose simplexes are the vertex sets of the complete subgraphs of G. Here we study a sufficient condition for G<FONT FACE=Symbol>­</FONT> and K(G)<FONT FACE=Symbol>­</FONT> to be homotopic. Applying this result to Whitney triangulations of surfaces, we construct an infinite family of examples which solve in the affirmative Prisner's open problem 1 in Graph Dynamics (Longman, Harlow, 1995): Are there finite connected graphs G that are periodic under K and where the second modulo 2 Betti number is greater than 0?
publishDate 2001
dc.date.none.fl_str_mv 2001-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002001000200010
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002001000200010
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0104-65002001000200010
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Computação
publisher.none.fl_str_mv Sociedade Brasileira de Computação
dc.source.none.fl_str_mv Journal of the Brazilian Computer Society v.7 n.3 2001
reponame:Journal of the Brazilian Computer Society
instname:Sociedade Brasileira de Computação (SBC)
instacron:UFRGS
instname_str Sociedade Brasileira de Computação (SBC)
instacron_str UFRGS
institution UFRGS
reponame_str Journal of the Brazilian Computer Society
collection Journal of the Brazilian Computer Society
repository.name.fl_str_mv Journal of the Brazilian Computer Society - Sociedade Brasileira de Computação (SBC)
repository.mail.fl_str_mv jbcs@icmc.sc.usp.br
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