2000•Journal of Graph TheoryRequires access

Clique-inverse graphs ofK3-free andK4-free graphs

Fábio Protti, Jayme L. Szwarcfiter

Abstract

The clique graph K(G) of a given graph G is the intersection graph of the collection of maximal cliques of G. Given a family ℱ of graphs, the clique-inverse graphs of ℱ are the graphs whose clique graphs belong to ℱ. In this work, we describe characterizations for clique-inverse graphs of K3-free and K4-free graphs. The characterizations are formulated in terms of forbidden induced subgraphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 257–272, 2000

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Key concepts: Combinatorics, Mathematics, Split graph, Clique-sum, Chordal graph, Cograph, Block graph, Indifference graph