P5-free augmenting graphs and the maximum stable set problem

P5-free augmenting graphs and the maximum stable set problem

The complexity status of the maximum stable set problem in the class of P5-free graphs is unknown. In this paper, we 3rst propose a characterization of all connected P5-free augmenting graphs. We then use this characterization to detect families of subclasses of P5-free graphs where the maximum stable set problem has a polynomial time solution. These families extend several previously studied c...

An augmenting graph approach to the stable set problem in P5-free graphs

The maximum weight stable set problem in $(P_6, \mbox{bull})$-free graphs

We present a polynomial-time algorithm that finds a maximum weight stable set in a graph that does not contain as an induced subgraph an induced path on six vertices or a bull (the graph with vertices a, b, c, d, e and edges ab, bc, cd, be, ce).

Maximum Weight Stable Set in ($P_7$, bull)-free graphs

We give a polynomial time algorithm that finds the maximum weight stable set in a graph that does not contain an induced path on seven vertices or a bull (the graph with vertices a, b, c, d, e and edges ab, bc, cd, be, ce). With the same arguments with also give a polynomial algorithm for any graph that does not contain S1,2,3 or a bull.

Weighted Parameters in (P5, P5)-free Graphs

We use the modular decomposition to give O(n(m + n)) algorithms for finding a maximum weighted clique (respectively stable set) and an approximate weighted colouring (respectively partition into cliques) in a (P5, P5)-free graph. As a by-product, we obtain an O(m+n) algorithm for finding a minimum weighted transversal of the C5 in a (P5, P5)free graph.