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

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 1, page 191-196
- ISSN: 2083-5892

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topHajime Matsumura. "On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k." Discussiones Mathematicae Graph Theory 35.1 (2015): 191-196. <http://eudml.org/doc/271232>.

@article{HajimeMatsumura2015,

abstract = {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.},

author = {Hajime Matsumura},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {spanning tree; degree bounded tree; degree sum condition},

language = {eng},

number = {1},

pages = {191-196},

title = {On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k},

url = {http://eudml.org/doc/271232},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Hajime Matsumura

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

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 1

SP - 191

EP - 196

AB - 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.

LA - eng

KW - spanning tree; degree bounded tree; degree sum condition

UR - http://eudml.org/doc/271232

ER -

## References

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