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.
@article{bwmeta1.element.doi-10_7151_dmgt_1778,
author = {Hajime Matsumura},
title = {On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {191-196},
zbl = {1307.05052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1778}
}
Hajime Matsumura. On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 191-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1778/
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