Local and Global Clique Numbers

Local and Global Clique Numbers

Clique numbers of graphs

Many graph-theoretical problems involve the study of cliques, i .e ., complete subgraphs (not necessarily maximal) . In this context the following combinatorial problem arises naturally: For which numbers n and c is there a graph with n vertices and exactly c cliques? For fixed n, let G(n) denote the set of all such `clique numbers' c . Since each singleton and the empty set are always cliques,...

Clique-graph matching by preserving global & local structure

This paper originally proposes the clique-graph and further presents a clique-graph matching method by preserving global and local structures. Especially, we formulate the objective function of clique-graph matching with respective to two latent variables, the clique information in the original graph and the pairwise clique correspondence constrained by the one-to-one matching. Since the object...

Clique numbers of graph unions

Let B and R be two simple graphs with vertex set V , and let G(B, R) be the simple graph with vertex set V , in which two vertices are adjacent if they are adjacent in at least one of B and R. For X ⊆ V , we denote by B|X the subgraph of B induced by X; let R|X and G(B, R)|X be defined similarly. We say that the pair (B, R) is additive if for every X ⊆ V , the sum of the clique numbers of B|X a...

Greedy clique decompositions and the Turán numbers

an Numbers Sean McGuinness University of Ume a September, 1994 Abstract. In this paper, we show that for p 4 if C is a clique decomposition obtained by removing maximal cliques(ie. their edges) of order at least p one by one until none remain, in which case the remaining edges are removed one by one, then the sum of the orders of the cliques in C is at most 2tp 1(n): Here tp 1(n) denotes the nu...