ORIENTED CYCLES IN DIGRAPHS OF LARGE OUTDEGREE

In 1985, Mader conjectured that for every acyclic digraph F there exists K = K(F) such that every digraph D with minimum out-degree at least K contains a subdivision of F. This conjecture remains widely open, even for digraphs F on five vertices. Recently, Aboulker, Cohen, Havet, Lochet, Moura and T...

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Published inCombinatorica (Budapest. 1981) Vol. 42; no. S1; p. 1145
Main Authors Gishboliner, Lior, Steiner, Raphael, Szabo, Tibor
Format Journal Article
LanguageEnglish
Published Springer 15.12.2022
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Summary:In 1985, Mader conjectured that for every acyclic digraph F there exists K = K(F) such that every digraph D with minimum out-degree at least K contains a subdivision of F. This conjecture remains widely open, even for digraphs F on five vertices. Recently, Aboulker, Cohen, Havet, Lochet, Moura and Thomasse studied special cases of Mader's problem and made the following conjecture: for every l [greater than or equal to] 2 there exists K = K(l) such that every digraph D with minimum out-degree at least K contains a subdivision of every orientation of a cycle of length l. We prove this conjecture and answer further open questions raised by Aboulker et al.
ISSN:0209-9683
DOI:10.1007/[s.sub.0]0493-021-4750-z