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Degree-square Turán problem for two self-converse tournaments
Abstract
For a fixed digraph F, let ex2+(n,F) be the maximum of ∑v∈ V(D)dD+(v)2 over all n-vertex F-free digraphs. Ai et al. [arXiv:2606.03520, 2026] asked for which self-converse tournament F one can determine ex2+(n,F). Let TTr denote a transitive tournament on r vertices and RT5 denote a regular tournament on 5 vertices. Note that both TTr and RT5 are self-converse. Iľkovič [arXiv:2609.05042, 2026] determined ex2+(n,F) for F=TT4. In this paper, we determine ex2+(n,F) for F being TTr or RT5, and the latter confirms a conjecture due to Iľkovič.
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BibTeX
@misc{han2026degreesquare,
title = {{Degree-square Turán problem for two self-converse tournaments}},
author = {Zhuoran Han and Yaojun Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01047},
eprint = {2610.01047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01047},
}
RIS
TY - UNPB
TI - Degree-square Turán problem for two self-converse tournaments
AU - Zhuoran Han
AU - Yaojun Chen
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01047
UR - https://arxiv.org/abs/2610.01047
AB - For a fixed digraph F, let ex_2^+(n,F) be the maximum of ∑_v∈ V(D)d_D^+(v)^2 over all n-vertex F-free digraphs. Ai et al. [arXiv:2606.03520, 2026] asked for which self-converse tournament F one can determine ex_2^+(n,F). Let TT_r denote a transitive tournament on r vertices and RT_5 denote a regular tournament on 5 vertices. Note that both TT_r and RT_5 are self-converse. Iľkovič [arXiv:2609.05042, 2026] determined ex_2^+(n,F) for F=TT_4. In this paper, we determine ex_2^+(n,F) for F being TT_r or RT_5, and the latter confirms a conjecture due to Iľkovič.
ER -