Proof of a conjecture of Alan Hartman

Abstract

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 K2m, where m ≥ 4, there exists a (2m - 1)-edge-coloring of K2m such that all the edges of T receive distinct colors if and only if T is good. © 1999 John Wiley & Sons, Inc.