Let k be a non-negative integer. A branch vertex of a tree is a vertex of degree at least three. We show two sufficient conditions for a connected clawfree graph to have a spanning tree with aâ€¦ (More)

Let 1 a < b be integers and G a graph of order n sufficiently large for a and b. Then G has an [a, b]-factor if the minimum degree is at least a and every pair of vertices distance two apart hasâ€¦ (More)

For a graph H and an integer k â‰¥ 2, let Ïƒk(H) denote the minimum degree sum of k independent vertices of H. We prove that if a connected claw-free graph G satisfies Ïƒk+1(G) â‰¥ |G| âˆ’ k, then G has aâ€¦ (More)

Let G be a graph and W a subset of V (G). Let g, f : V (G) â†’ Z be two integer-valued functions such that g(x) â‰¤ f(x) for all x âˆˆ V (G) and g(y) â‰¡ f(y) (mod 2) for all y âˆˆ W . Then a spanning subgraphâ€¦ (More)