A note on matching-cut in P-free graphs

A note on minimal matching covered graphs

A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.

Cut-Matching Games on Directed Graphs

We give O(log n)-approximation algorithm based on the cut-matching framework of [10, 13, 14] for the computing the sparsest cut on directed graphs. Our algorithm uses only O(log n) single commodity max-flow computations and thus breaks the multicommodity-flow barrier for computing the sparsest cut on directed graphs.

A note on vague graphs

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

A note on contracting claw-free graphs

A graph containment problem is that of deciding whether one graph called the host graph can be modified into some other graph called the target graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex deletions and vertex dissolutions as possible graph operations permitted. By allowing any combination of these four operations we capture the fo...

A Note on Triangle-Free Graphs