Spanning k-ended trees of bipartite graphs

Mikio Kano, Haruhide Matsuda, Masao Tsugaki, Guiying Yan

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A tree is called a k-ended tree if it has at most k leaves, where a leaf is a vertex of degree one. We prove the following theorem. Let k≥2 be an integer, and let G be a connected bipartite graph with bipartition (A,B) such that |A|≤|B|≤|A|+k-1. If σ2(G)≥(|G|-k+2)/2, then G has a spanning k-ended tree, where σ2(G) denotes the minimum degree sum of two non-adjacent vertices of G. Moreover, the condition on σ2(G) is sharp. It was shown by Las Vergnas, and Broersma and Tuinstra, independently that if a graph H satisfies σ2(H) ≥|H|-k+1 then H has a spanning k-ended tree. Thus our theorem shows that the condition becomes much weaker if a graph is bipartite.

Original languageEnglish
Pages (from-to)2903-2907
Number of pages5
JournalDiscrete Mathematics
Volume313
Issue number24
DOIs
Publication statusPublished - 2013 Oct 7

Keywords

  • Spanning k-ended tree
  • Spanning tree
  • Spanning tree with at most k leaves

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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