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On the largest tree of given maximum degree in a connected graph

✍ Scribed by Y. Caro; I. Krasikov; Y. Roditty

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 258 KB
Volume: 15
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190150103

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We prove that every connected graph G contains a tree T of maximum degree at most k that either spans G or has order at least __k__δ(G) + 1, where δ(G) is the minimum degree of G. This generalizes and unifies earlier results of Bermond [1] and Win [7]. We also show that the square of a connected graph contains a spanning tree of maximum degree at most three.

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