Abstract
A complete set of a graph G is a subset of V inducing a complete subgraph. A clique is a maximal complete set. Denote by \({\mathcal{C}}(G)\) the clique family of G. The clique graph of G, denoted by K(G), is the intersection graph of \(\mathcal{{C}}(G)\). Say that G is a clique graph if there exists a graph H such that G=K(H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. We prove that the clique graph recognition problem is NP-complete.
Dedicated to Alberto Santos Dumont, aviation pioneer, on the 100th anniversary of the flight of his 14 Bis in Paris in October 1906.
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Alcón, L., Faria, L., de Figueiredo, C.M.H., Gutierrez, M. (2006). Clique Graph Recognition Is NP-Complete. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_24
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DOI: https://doi.org/10.1007/11917496_24
Publisher Name: Springer, Berlin, Heidelberg
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