Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-04-01

Journal: ARS COMBINATORIA

Included Journals: SCIE

Volume: 138

Page Number: 161-170

ISSN: 0381-7032

Key Words: Spanning 3-ended tree; Quasi-claw-free graph; Insertible vertex

Abstract: Let sigma(k)(G) denote the minimum degree sum of k independent vertices of a graph G. A spanning tree with at most m leaves is called a spanning m-ended tree. A graph is quasi-claw-free if for any two vertices x, y with d(x, y) = 2, there exists a vertex u such that u is an element of N (x) boolean AND N (y), N (u) subset of N [x] boolean OR N[y]. In this paper, we prove that for any k-connected quasi-claw-free graph G with order n, if sigma(k+3)(G) >= n - k, then G contains a spanning 3-ended tree.