We consider degree sum conditions and the existence of vertex-disjoint cycles in a graph. In this paper, we prove the following: Suppose that G is a graph of order at least 3k + 2 and Ïƒ3(G) â‰¥ 6k âˆ’ 2,â€¦ (More)

In this paper, we prove that an m-connected graph G on n vertices has a spanning tree with at most k leaves (for k â‰¥ 2 and m â‰¥ 1) if every independent set of G with cardinality m+k contains at leastâ€¦ (More)

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)

In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n â‰¥ 1, k â‰¥ 3, c â‰¥ 0 and G be an n-connected graph. Suppose that for every independent set S âŠ†â€¦ (More)

For a graph G, p(G) and c(G) denote the orders of a longest path and a longest cycle of G, respectively. For a graph G, we denote by dG(x) and Îº(G) the degree of a vertex x in G and the connectivityâ€¦ (More)

123 Abstract In recent years, the demand of quality software products has been increasing rapidly. At the same time, the delivery period is becoming more and more shorter in spite of high-qualityâ€¦ (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)