Uniformly resolvable ${P_4, C_k}$-decomposition of $K_n$ - a complete solution
Abstract
Let $K_n,$ $C_{n}$, and $P_{n}$ respectively denote the complete graph, cycle and path on $n$ vertices. Uniformly resolvable decomposition of $K_n$ is a decomposition of $K_n$ into subgraphs which can be partitioned into factors containing pairwise isomorphic subgraphs.
In this paper, we determine necessary and sufficient conditions for the existence of uniformly resolvable decomposition of $K_n$ into $P_4$ and $C_k,~ k\geq3.$
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