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Ramsey--Turán Factors of Non-directed Oriented Cycles in Oriented Graphs
Abstract
Let overrightarrowC be any orientation of the cycle Cℓ which is not directed. We prove that, for every integer ℓ≥3 and every μ>0, there is a real γ such that every sufficiently large oriented graph D with ℓ| |D|, minimum semidegree at least (1/4+μ)|D| and independence number at most γ|D| has a overrightarrowC-factor. The constant 1/4 is asymptotically tight. This proof establishes Ramsey-Turán type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.
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BibTeX
@misc{zhou2026ramseyturán,
title = {{Ramsey--Turán Factors of Non-directed Oriented Cycles in Oriented Graphs}},
author = {Jia Zhou and Yunshu Gao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.08591},
eprint = {2608.08591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08591},
}
RIS
TY - UNPB
TI - Ramsey--Turán Factors of Non-directed Oriented Cycles in Oriented Graphs
AU - Jia Zhou
AU - Yunshu Gao
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.08591
UR - https://arxiv.org/abs/2608.08591
AB - Let overrightarrowC be any orientation of the cycle C_ℓ which is not directed. We prove that, for every integer ℓ≥3 and every μ>0, there is a real γ such that every sufficiently large oriented graph D with ℓ| |D|, minimum semidegree at least (1/4+μ)|D| and independence number at most γ|D| has a overrightarrowC-factor. The constant 1/4 is asymptotically tight. This proof establishes Ramsey-Turán type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.
ER -