 
Summary: Discrete Applied Mathematics 27 (1990) 2528
NorthHolland
25
UNIVERSAL SEQUENCES FOR COMPLETE GRAPHS
N. ALON
Bell Communications Research, Morristown, NJ 07960, USA; Department of Mathematics,
Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
Y. AZAR and Y. RAVID
Department of Computer Science, Sackler Faculty of Exact Sciences, Tel Aviv University,
Ramat Aviv, Tel Aviv, Israel
Received 30 May 1989
An nlabeled complete digraph G is a complete digraph with n + 1 vertices and n(n + 1) edges
labeled {1,2, ... ,n} such that there is a unique edge of each label emanating from each vertex.
A sequence S in {1,2, .. . , n} * and a starting vertex of G define a unique walk in G, in the obvious
way. Suppose S is a sequence such that for each such G and each starting point in it, the
corresponding walk contains all the vertices of G. We show that the length of S is at least Q(n2),
improving a previously known n(n log2n/loglogn) lower bound of BarNoy, Borodin,
Karchmer, Linial and Werman.
1. Introduction
For n I 2 an nlabeled complete directed graph G is a directed graph with n + 1
