Minimum covering by triples, quadruples and quintuples with minimum excess
Combinatorics
2026-03-20 v1
Abstract
This article explores a new type of optimal covering of a complete graph by small cliques of different sizes, namely the minimum covering with minimum excess. In particular, the minimum size of a covering by triples and quadruples with minimum excess is determined. Moreover, some generalisation onto minimum coverings by triples, quadruples and quintuples with minimum excess is presented.
Cite
@article{arxiv.2603.18803,
title = {Minimum covering by triples, quadruples and quintuples with minimum excess},
author = {Petr Kovář and Yifan Zhang},
journal= {arXiv preprint arXiv:2603.18803},
year = {2026}
}