3-Colorability ∈P for P6-free graphs

3-Colorability in P for P6-free graphs

4-colorability of P6-free graphs

In this paper we will study the complexity of 4-colorability in subclasses of P6-free graphs. The well known k-colorability problem is NP -complete. It has been shown that if k-colorability is solvable in polynomial time for an induced H-free graph, then every component of H is a path. Recently, Huang [11] has shown several improved complexity results on k-coloring Pt-free graphs, where Pt is a...

Vertex 3-colorability of Claw-free Graphs

The 3-colorability problem is NP-complete in the class of clawfree graphs and it remains hard in many of its subclasses obtained by forbidding additional subgraphs. (Line graphs and claw-free graphs of vertex degree at most four provide two examples.) In this paper we study the computational complexity of the 3-colorability problem in subclasses of claw-free graphs defined by finitely many forb...

A Certifying Algorithm for 3-Colorability of P5-Free Graphs

We provide a certifying algorithm for the problem of deciding whether a P5-free graph is 3-colorable by showing there are exactly six finite graphs that are P5-free and not 3-colorable and minimal with respect to this property.

Stable sets for (P6, K2, 3)-free graphs

The Maximum Stable Set (MS) problem is a well known NP-hard problem. However different graph classes for which MS can be efficiently solved have been detected and the augmenting graph technique seems to be a fruitful tool to this aim. In this paper we apply a recent characterization of minimal augmenting graphs [22] to prove that MS can be solved for (P6,K2,3)-free graphs in polynomial time, ex...