TY - JOUR

T1 - Oriented Cycles in Digraphs of Large Outdegree

AU - Gishboliner, Lior

AU - Steiner, Raphael

AU - Szabó, Tibor

N1 - Publisher Copyright:
© 2022, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.

PY - 2022/12

Y1 - 2022/12

N2 - 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 Thomassé studied special cases of Mader’s problem and made the following conjecture: for every ℓ ≥ 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.

AB - 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 Thomassé studied special cases of Mader’s problem and made the following conjecture: for every ℓ ≥ 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.

UR - http://www.scopus.com/inward/record.url?scp=85130500102&partnerID=8YFLogxK

U2 - 10.1007/s00493-021-4750-z

DO - 10.1007/s00493-021-4750-z

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85130500102

SN - 0209-9683

VL - 42

SP - 1145

EP - 1187

JO - Combinatorica

JF - Combinatorica

ER -