A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a ...
An even-hole-free graph is a graph that does not contain, as an induced subgraph, a chordless cycle of even length. A graph is triangulated if it does not contain any chordless cy...
In this paper, we consider two facility location problems on tree networks. One is the 2-radius problem, whose goal is to partition the vertex set of the given network into two no...
Let ir(G) and (G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H) = (H), for every induced subgr...
Let G be a graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it k-colorable. It is shown that in this case most induced subgraphs of G on c...