Optimal decomposition of $K_{18}$ and $K_{19}$ into $K_3$ and $K_4$
Petr Kov\'a\v{r}, Yifan Zhang
TL;DR
This paper presents a novel method for optimally decomposing complete graphs of order 18 and 19 into smaller cliques of sizes 3 and 4, advancing combinatorial design theory.
Contribution
It introduces a new approach to achieve optimal decompositions of specific complete graphs into smaller complete subgraphs, improving upon existing methods.
Findings
Successfully decomposed K_18 and K_19 into K_3 and K_4
Established optimality criteria for such decompositions
Provides a constructive method for similar problems
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Finite Group Theory Research