On heterochromatic out-directed spanning trees in tournaments

TL;DR

This paper determines the exact minimum number of colors needed in any arc-coloring of a tournament to guarantee an out-directed spanning tree with all arcs uniquely colored.

Contribution

It provides the precise value of h(T), the minimum number of colors ensuring a heterochromatic out-directed spanning tree in any tournament.

Findings

Exact value of h(T) for any tournament T

Characterization of colorings guaranteeing heterochromatic spanning trees

Extension of previous bounds to exact thresholds

Abstract

Given a tournament T, let h(T) be the smallest integer k such that every arc-coloring of T with k or more colors produces at least one out-directed spanning tree of T with no pair of arcs with the same color. In this paper we give the exact value of h(T).