Packing 4-cycles in Eulerian and bipartite Eulerian tournaments with an application to distances in interchange graphs

Raphael Yuster

doi:10.1007/s00026-005-0244-0

Packing 4-cycles in Eulerian and bipartite Eulerian tournaments with an application to distances in interchange graphs

Raphael Yuster

Department of Mathematics

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

Abstract

We prove that every Eulerian orientation of K _m,n contains 1/4+√8mn(1 o(1)) arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains 1/8+√32n ²(1 o(1)) arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between two antipodal vertices in interchange graphs.

Original language	English
Pages (from-to)	117-124
Number of pages	8
Journal	Annals of Combinatorics
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s00026-005-0244-0
State	Published - Apr 2005

Keywords

Cycles
Interchange graphs
Packing
Tournaments

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1007/s00026-005-0244-0

Cite this

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abstract = "We prove that every Eulerian orientation of K m,n contains 1/4+√8mn(1 o(1)) arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains 1/8+√32n 2(1 o(1)) arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between two antipodal vertices in interchange graphs.",

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AB - We prove that every Eulerian orientation of K m,n contains 1/4+√8mn(1 o(1)) arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains 1/8+√32n 2(1 o(1)) arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between two antipodal vertices in interchange graphs.

KW - Cycles

KW - Interchange graphs

KW - Packing

KW - Tournaments

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Packing 4-cycles in Eulerian and bipartite Eulerian tournaments with an application to distances in interchange graphs

Abstract

Keywords

ASJC Scopus subject areas

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