Almost given length cycles in digraphs

Raphael Yuster

doi:10.1007/s00373-007-0769-1

Almost given length cycles in digraphs

Raphael Yuster

Department of Mathematics

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

Abstract

A digraph is called k-cyclic if it cannot be made acyclic by removing less than k arcs. It is proved that for every ε > 0 there are constants K and δ so that for every d (0, δn), every ε n ²-cyclic digraph with n vertices contains a directed cycle whose length is between d and d + K. A more general result of the same form is obtained for blow-ups of directed cycles.

Original language	English
Pages (from-to)	59-65
Number of pages	7
Journal	Graphs and Combinatorics
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00373-007-0769-1
State	Published - Feb 2008

Keywords

Directed cycle
Directed graph
Regularity lemma

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-007-0769-1

Cite this

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abstract = "A digraph is called k-cyclic if it cannot be made acyclic by removing less than k arcs. It is proved that for every ε > 0 there are constants K and δ so that for every d (0, δn), every ε n 2-cyclic digraph with n vertices contains a directed cycle whose length is between d and d + K. A more general result of the same form is obtained for blow-ups of directed cycles.",

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AB - A digraph is called k-cyclic if it cannot be made acyclic by removing less than k arcs. It is proved that for every ε > 0 there are constants K and δ so that for every d (0, δn), every ε n 2-cyclic digraph with n vertices contains a directed cycle whose length is between d and d + K. A more general result of the same form is obtained for blow-ups of directed cycles.

KW - Directed cycle

KW - Directed graph

KW - Regularity lemma

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M3 - Article

AN - SCOPUS:43049084064

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JF - Graphs and Combinatorics

IS - 1

ER -

Almost given length cycles in digraphs

Abstract

Keywords

ASJC Scopus subject areas

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