Hits:

Indexed by:期刊论文

Date of Publication:2018-04-01

Journal:ARS COMBINATORIA

Included Journals:SCIE

Volume:138

Page Number:161-170

ISSN No.: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.