Local transformations of graphs preserving independence number

Stability preserving transformations of graphs

Graph transformations proved useful for many algorithmic problems. In the present paper, we study this tool with respect to the maximum stable set problem. We first review available results on this topic and then propose an approach to uniformly describe and systematically develop graph transformations that do not change the size of a maximum stable set in the graph. The approach is illustrated...

Graph transformations preserving the stability number

We analyse the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin deletions. We also show how some of these transformations are related to the notion of even pair introduced to color some classes of perfect gr...

Semi-regular graphs of minimum independence number

There are many functions of the degree sequence of a graph which give lower bounds on the independence number of the graph. In particular, for every graph G, α(G) ≥ R(d(G)), where R is the residue of the degree sequence of G. We consider the precision of this estimate when it is applied to semi-regular degree sequences. We show that the residue nearly always gives the best possible estimate on ...

On the independence number of random graphs

Independence Number and Disjoint Theta Graphs

The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a θ-graph to be a pair of vertices u, v with three internally disjoint paths joining u to v. Given an independence number α and a fixed integer k, the results contained in this paper provide sharp bounds on the order f(k, α) of a graph with independence number α(G) ≤ α which contains no k disjoint ...