# Spanning k-ended trees of bipartite graphs

Mikio Kano, Haruhide Matsuda, Masao Tsugaki, Guiying Yan

3 被引用数 (Scopus)

## 抄録

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.

本文言語 English 2903-2907 5 Discrete Mathematics 313 24 https://doi.org/10.1016/j.disc.2013.09.002 Published - 2013

## ASJC Scopus subject areas

• 理論的コンピュータサイエンス
• 離散数学と組合せ数学

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