For a given graph G of n vertices and m edges, a clique S of size k is said to be c-isolated if there are at most ck outgoing edges from S. It is shown that this parameter c is an interesting measure which governs the complexity of finding cliques. In particular, if c is a constant, then we can enumerate all c-isolated maximal cliques in linear time, and if c = O(log n), then we can enumerate all c-isolated maximal cliques in polynomial time. Note that there is a graph which has a superlinear number of c-isolated cliques if c is not a constant, and there is a graph which has a superpolynomial number of c-isolated cliques if c = ω(log n). In this sense our algorithm is optimal for the linear-time and polynomialtime enumeration of c-isolated cliques. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Ito, H., Iwama, K., & Osumi, T. (2005). Linear-time enumeration of isolated cliques. In Lecture Notes in Computer Science (Vol. 3669, pp. 119–130). Springer Verlag. https://doi.org/10.1007/11561071_13
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