We say a graph G is minimal with respect to a property Q if there exists no proper induced subgraph G' of G with property Q. In this paper we characterize all minimal graphs with respect to theâ€¦ (More)

We study the stability of some classes of graphs deened in terms of forbidden sub-graphs under the closure operation introduced by the second author. Using these results, we prove that everyâ€¦ (More)

In this paper we characterize all triples of connected graphs C; X; Y (where C is a claw) and such that every 2-connected CXY -free graph G is hamiltonian.This result together with a previous resultâ€¦ (More)

We study the stability of some classes of claw-free graphs deened in terms of forbidden subgraphs under the closure operation deened in 10]. We characterize all connected graphs A such that the classâ€¦ (More)

A generalized (i; j; k)-net N i;j;k is the graph obtained by identifying each of the vertices of a triangle with an endvertex of one of three vertex-disjoint paths of lengths i; j; k. We prove thatâ€¦ (More)

A connected edge-colored graph G is rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors; the rainbow connection number rc(G) of G isâ€¦ (More)