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Summary: JOURNAL OF COMBINATORIAL THEORY, %XieS B 47, 114-l 19 (1989)
Note
Cycles of Length 0
Modulo k in Directed Graphs
NOGA ALON*
School of Mathematical Sciences, Sackler Faculty of Exact Sciences,
Tel Aviv University, Tel Aviv, Israel
AND
N. LINIAL
Institute of Mathematics, The Hebrew University
Jerusalem, Israel
of Jerusalem,
Communicated by J. A. Bondy
Received November 19, 1987
We show that every digraph D with minimum outdegree 6 and maxi-
mum indegree A contains a directed cycle of length O(mod k), provided
e[dd+ l]( 1- l/k)" < 1. In particular, if A < (2" - e)/e6 then D contains an even
cycle. 0 1989 Academic Press, Inc.
1. INTRODUCTION
The problem of deciding whether a given directed graph contains an
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