PreprintCC BY 4.0arXiv
Turán number of three disjoint cliques of arbitrary sizes
Abstract
The Turán number ex(n,H) of a given graph H is the maximum number of edges in an n-vertex H-free graph. In this paper, for all p≥ q≥ r≥ 2 and n≥ p+q+r, we determine the exact value of ex(n,Kp∪ Kq∪ Kr) and describe all extremal graphs.
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BibTeX
@misc{kostochka2026turán,
title = {{Turán number of three disjoint cliques of arbitrary sizes}},
author = {Alexandr Kostochka and Dadong Peng and Zimu Xiang and Liang Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38430},
eprint = {2610.38430},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38430},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Turán number of three disjoint cliques of arbitrary sizes
AU - Alexandr Kostochka
AU - Dadong Peng
AU - Zimu Xiang
AU - Liang Zhang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38430
UR - https://arxiv.org/abs/2610.38430
AB - The Turán number ex(n,H) of a given graph H is the maximum number of edges in an n-vertex H-free graph. In this paper, for all p≥ q≥ r≥ 2 and n≥ p+q+r, we determine the exact value of ex(n,K_p∪ K_q∪ K_r) and describe all extremal graphs.
ER -