The problem of computing the chromatic number of a P 5-free graph (aÂ graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show that for every fixedâ€¦ (More)

Vertex and edge colorability are two graph problems that are NP-hard in general. We show that both problems remain difficult even for graphs without short cycles, i.e., without cycles of length atâ€¦ (More)

Whether the clique-width of graphs in a certain class of graphs is bounded or not is an important question from an algorithmic point of view, as many problems that are NP-hard in general admitâ€¦ (More)

The class of fork-free graphs is an extension of claw-free graphs and their subclass of line graphs. The first polynomial-time solution to the maximum weight independent set problem in the class ofâ€¦ (More)

In this paper, we provide complete classification of classes of bipartite graphs defined by a single forbidden induced bipartite subgraph with respect to bounded/unbounded clique-width.

Bipartite permutation graphs have several nice characterizations in terms of vertex ordering. Besides, as AT-free graphs, they have a linear structure in the sense that any connected bipartiteâ€¦ (More)