On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k

• Autorzy: Hajime Matsumura
• Języki publikacji: EN

Abstrakty

EN

A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σk(G) ≥ |V (G)|+s−1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree less than k. The degree condition is sharp.

Słowa kluczowe

EN

spanning tree; degree bounded tree; degree sum condition

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 1
• Strony: 191-196

Daty

wydano

2015-02-01

otrzymano

2013-10-16

poprawiono

2014-01-31

zaakceptowano

2014-01-31

online

2015-02-06

Twórcy

autor

Hajime Matsumura

• College of Education Ibaraki University Ibaraki 310-8512, Japan

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1778