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Optimal decomposition of $K_{18}$ and $K_{19}$ into $K_3$ and $K_4$

Combinatorics 2025-07-10 v1
Authors: Petr Kovář , Yifan Zhang
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Abstract

This article explores a new way to obtain the optimal decomposition of a complete graph of order 18 and 19 into cliques of order 3 and 4.

Keywords

complete graph clique decomposition $K_3$ $K_4$ $K_{18}$ $K_{19}$

Cite

@article{arxiv.2507.06745,
  title  = {Optimal decomposition of $K_{18}$ and $K_{19}$ into $K_3$ and $K_4$},
  author = {Petr Kovář and Yifan Zhang},
  journal= {arXiv preprint arXiv:2507.06745},
  year   = {2025}
}

Comments

paper 25 pages, appendix 37 pages

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