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
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AN - SCOPUS:85130500102
SN - 0209-9683
VL - 42
SP - 1145
EP - 1187
JO - Combinatorica
JF - Combinatorica
ER -