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Euler tours and a game with dominoes

✍ Scribed by Victor Neumann-Lara; Eduardo Rivera-Campo

Book ID: 104113773
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 330 KB
Volume: 167-168
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00252-x

No coin nor oath required. For personal study only.

✦ Synopsis

Let K'n denote the complete graph with vertices v0, Vl,...,/)n-l, together with the loops ei =/)ivi for i = 0, 1 ..... n -1. Suppose n = 3 mod 4 and that the edges of K~ are coloured either blue or red in such a way that each colour class has the same number of edges. We show that there is an ordering fl, f2,..., f,, of the edges of K;,, alternating colours, such that for i = 1,2 ..... rn 1, the edges fl, f2 .... , f. form a trail Ti of K~, with /]+1 incident with at least one end of Ti. This solves a problem proposed by Gonzfilez-Acufia and Urrutia (1985).

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