On P5-free Chordal bipartite graphs

Maximum induced matching problem on hhd-free graphs

An induced matching in a graph is a set of edges such that no two edges in the set are joined by any third edge of the graph. An induced matching is maximum (MIM) if the number of edges in it is the largest among all possible induced matchings. It is known that finding the size of a MIM in a graph is NP-hard even if the graph is bipartite. It is also known that the size of a MIM in a chordal gr...

Chordal bipartite graphs of bounded tree- and clique-width

A bipartite graph is chordal bipartite if every cycle of length at least six has a chord. In the class of chordal bipartite graphs the tree-width and the clique-width are unbounded. Our main results are that chordal bipartite graphs of bounded vertex degree have bounded tree-width and that k-fork-free chordal bipartite graphs have bounded clique-width, where a k-fork is the graph arising from a...

Graphs with complete minimal k-vertex separators

G. A. Dirac characterized chordal graphs as those in which minimal vertex separators always induce complete subgraphs. I generalize a traditional (2-)vertex separator to a k-vertex separator — meaning a set S of vertices whose removal puts k independent vertices into k separate components. Generalizing Dirac’s theorem, the {P5, 2P3}-free chordal graphs are the graphs in which minimal k-separato...

Parallel Algorithms For Recognizing P5-Free And P5-Free Weakly Chordal Graphs

On weighted efficient total domination

An efficiently total dominating set of a graph G is a subset of its vertices such that each vertex of G is adjacent to exactly one vertex of the subset. If there is such a subset, then G is an efficiently total dominable graph (G is etd). In this paper, we prove NP-completeness of the etd decision problem on the class of planar bipartite graphs of maximum degree 3. Furthermore, we give an effic...