A note on the number of edges guaranteeing a C4 in Eulerian bipartite digraphs

Jian Shen; Raphael Yuster

doi:10.37236/1667

A note on the number of edges guaranteeing a C₄ in Eulerian bipartite digraphs

Jian Shen
, Raphael Yuster

Department of Mathematics

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

Abstract

Let G be an Eulerian bipartite digraph with vertex partition sizes m, n. We prove the following Turán-type result: If e(G) > 2mn/3 then G contains a directed cycle of length at most 4. The result is sharp. We also show that if e(G) = 2mn/3 and no directed cycle of length at most 4 exists, then G must be biregular. We apply this result in order to obtain an improved upper bound for the diameter of interchange graphs.

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	Electronic Journal of Combinatorics
Volume	9
Issue number	1 N
DOIs	https://doi.org/10.37236/1667
State	Published - 2002

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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A note on the number of edges guaranteeing a C₄ in Eulerian bipartite digraphs

Abstract

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