In this paper we obtain some upper bounds for b-chromatic number of K1,t -free graphs, graphs with given minimum clique partition and bipartite graphs. These bounds are in terms of either clique number or chromatic number of graphs or biclique number for bipartite graphs. We show that all the bounds are tight. AMS Classification: 05C15.

‎in this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is cohen-macaulay‎. ‎it is proved that if there exists a cover of an $r$-partite cohen-macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

‎In this paper‎, ‎exact formulas for the dependence‎, ‎independence‎, ‎vertex cover and clique polynomials of the power graph and its‎ ‎supergraphs for certain finite groups are presented‎.

We give an O(n) algorithm to find a minimum clique cover of a (bull, C4)-free graph, or equivalently, a minimum colouring of a (bull, 2K2)-free graph, where n is the number of vertices of the graphs.

A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect in exactly p vertices. A graph G is said to have a p-regular k-clique cover if there is a p-regular family H of k-cliques of G such that each edge of G belongs to a clique in H. Such a p-regular kclique cover is separable if the complete subgraphs of order p that arise as intersections of pairs o...

In this paper, we are interested inminimizing the sum of block sizes in a pairwise balanced design, where there are some constraints on the size of one block or the size of the largest block. For every positive integers n,m, wherem ≤ n, letS (n,m) be the smallest integer s for which there exists a PBD on n points whose largest block has sizem and the sum of its block sizes is equal to s. Also, ...

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n) decomposition algorithm and we take advantage of the involution modular decomposition tree to state several algorithmic results. Cographs are the graphs that are totally decomposable w.r.t modular decomp...

Royal Road functions manipulate the t-ness landscape to provide controlled experiments into genetic algorithm (GA) theory Mitchell et al., 1992]. Variations of clique detection in a graph, e.g., nding both the max clique Soule et al., 1996] and the clique cover Haynes, 1996], have been proposed as naturally occurring Royal Road functions. Soule and Foster have tried to positively correlate diie...