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Proof of a conjecture of Alan Hartman

✍ Scribed by Liu, Q. Z.; Yap, H. P.

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 265 KB
Volume: 30
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199901)30:1<7::aid-jgt2>3.0.co;2-4

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✦ Synopsis

A tree T is said to be bad, if it is the vertex-disjoint union of two stars plus an edge joining the center of the first star to an end-vertex of the second star. A tree T is good, if it is not bad. In this article, we prove a conjecture of Alan Hartman that, for any spanning tree T of K 2m , where m ≥ 4, there exists a (2m -1)-edge-coloring of K 2m such that all the edges of T receive distinct colors if and only if T is good.

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