4-colorability of P6-free graphs

Complexity of Coloring Graphs without Paths and Cycles

Let Pt and C` denote a path on t vertices and a cycle on ` vertices, respectively. In this paper we study the k-coloring problem for (Pt, C`)-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada, have proved that 3-colorability of P5-free graphs has a finite forbidden induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and Vatshelle have shown that k-colorability of...

3-Colorability in P for P6-free graphs

Three complexity results on coloring P k - free graphs I

We prove three complexity results on vertex coloring problems restricted to Pk-free graphs, i.e., graphs that do not contain a path on k vertices as an induced subgraph. First of all, we show that the pre-coloring extension version of 5-coloring remains NP-complete when restricted to P6-free graphs. Recent results of Hoàng et al. imply that this problem is polynomially solvable on P5-free graph...

Three Complexity Results on Coloring Pk-Free Graphs

We prove three complexity results on vertex coloring problems restricted to Pk-free graphs, i.e., graphs that do not contain a path on k vertices as an induced subgraph. First of all, we show that the pre-coloring extension version of 5-coloring remains NP-complete when restricted to P6-free graphs. Recent results of Hoàng et al. imply that this problem is polynomially solvable on P5-free graph...

A New Characterization of P6-Free Graphs

The class of graphs that do not contain an induced path on k vertices, Pk-free graphs, plays a prominent role in algorithmic graph theory. This motivates the search for special structural properties of Pkfree graphs, including alternative characterizations. Let G be a connected Pk-free graph, k ≥ 4. We show that G admits a connected dominating set whose induced subgraph is either Pk−2-free, or ...