Given a graph G and an interdiction budget k∈N, the Edge Interdiction Clique Problem (EICP) asks to find subset of at most k edges remove from so that size maximum clique, in interdicted graph, is minimized. The EICP belongs family problems with aim reducing clique number graph. optimal solutions, called policies, determine vital which are crucial for preserving its number. We propose new set-c...

A clique-colouring of a graph G is a colouring of the vertices of G so that no maximal clique of size at least two is monochromatic. The clique-hypergraph, H(G), of a graph G has V (G) as its set of vertices and the maximal cliques of G as its hyperedges. A vertex-colouring of H(G) is a clique-colouring of G. Determining the clique-chromatic number, the least number of colours for which a graph...

A graph is perfect if the chromatic number of every induced subgraph equals the size of its largest clique, and an algorithm of Grötschel, Lovász, and Schrijver [9] from 1988 finds an optimal colouring of a perfect graph in polynomial time. But this algorithm uses the ellipsoid method, and it is a well-known open question to construct a “combinatorial” polynomial-time algorithm that yields an o...

In this paper we define the concept of clique number of uniform hypergraph and study its relationship with circular chromatic number and clique number. For every positive integer k,p and q, 2q ≤ p we construct a k-uniform hypergraph H with small clique number whose circular chromatic number equals p q . We define the concept and study the properties of c-perfect k-uniform hypergraphs .

We introduce a graph transformation which preserves the clique number. When applied to graphs containing no odd hole and no cricket (a particular graph on 5 vertices) the transformation also preserves the chromatic number. Using this transformation we derive a polynomial algorithm for the computation of the clique number of all graphs in a class which strictly contains diamond-free graphs. Furt...

A clique covering of a graph G is a set of cliques of G in which each edge of G is contained in at least one clique. The smallest cardinality of clique coverings of G is called the clique covering number of G. A glued graph results from combining two nontrivial vertex-disjoint graphs by identifying nontrivial connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the c...