Cycles of length 0 modulo k in directed graphs

Noga Alon; N. Linial

doi:10.1016/0095-8956(89)90071-3

Cycles of length 0 modulo k in directed graphs

Noga Alon^*
, N. Linial

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We show that every digraph D with minimum outdegree δ and maximum indegree Δ contains a directed cycle of length 0(mod k), provided e[Δd + 1](1 - 1 k)^δ < 1. In particular, if Δ < (2^δ - e) eδ the D contains an even cycle.

Original language	English
Pages (from-to)	114-119
Number of pages	6
Journal	Journal of Combinatorial Theory. Series B
Volume	47
Issue number	1
DOIs	https://doi.org/10.1016/0095-8956(89)90071-3
State	Published - Aug 1989

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title = "Cycles of length 0 modulo k in directed graphs",

abstract = "We show that every digraph D with minimum outdegree δ and maximum indegree Δ contains a directed cycle of length 0(mod k), provided e[Δd + 1](1 - 1 k)δ < 1. In particular, if Δ < (2δ - e) eδ the D contains an even cycle.",

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AB - We show that every digraph D with minimum outdegree δ and maximum indegree Δ contains a directed cycle of length 0(mod k), provided e[Δd + 1](1 - 1 k)δ < 1. In particular, if Δ < (2δ - e) eδ the D contains an even cycle.

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JO - Journal of Combinatorial Theory. Series B

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Cycles of length 0 modulo k in directed graphs

Abstract

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