In 1987, Akers, Harel and Krishnamurthy proposed the star graph Î£(n) as a new topology for interconnection networks. Hamiltonian properties of these graphs have been investigated by several authors.â€¦ (More)

Let G be a graph of order n with an edge coloring c, and let Î´(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least Î´(G) edgesâ€¦ (More)

A graph G is said to be claw-free if G has no induced subgraph isomorphic to K1,3. Matthews and Sumner [M. M. Matthews, D. P. Sumner, Longest paths and cycles in K1,3free graphs, J. Graph Theory 9â€¦ (More)

It is known that a 3-edge-connected graph has a spanning even subgraph in which every component contains at lest five vertices, and the lower bound is best possible. A natural question arises whetherâ€¦ (More)

In 1986, Thomassen posed the following conjecture: every 4-connected line graph has a Hamiltonian cycle. As a possible approach to the conjecture, many researchers have considered statements that areâ€¦ (More)