On hereditary clique-Helly self-clique graphs

Authors:
F. Larrión;M. A. Pizaña
Affiliations:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, México D.F. C.P. 04510, Mexico;Universidad Autónoma Metropolitana, Depto. de Ingeniería Eléctrica, Av. San Rafael Atlixco 186, Col Vicentina, México 09340 D.F., Mexico
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 3
Cited 2

A new characterization of strongly chordal graphs

Discrete Mathematics
On self-clique graphs with given clique sizes

Discrete Mathematics - Special issue on Combinatorics and Application
Self-clique graphs and matrix permutations

Journal of Graph Theory

The complexity of clique graph recognition

Theoretical Computer Science
Edge contraction and edge removal on iterated clique graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

A graph is clique-Helly if any family of mutually intersecting (maximal) cliques has non-empty intersection, and it is hereditary clique-Helly (HCH) if its induced subgraphs are clique-Helly. The clique graph of a graph G is the intersection graph of its cliques, and G is self-clique if it is connected and isomorphic to its clique graph. We show that every HCH graph is an induced subgraph of a self-clique HCH graph, and give a characterization of self-clique HCH graphs in terms of their constructibility starting from certain digraphs with some forbidden subdigraphs. We also specialize this results to involutive HCH graphs, i.e. self-clique HCH graphs whose vertex-clique bipartite graph admits a part-switching involution.