Kn(λ) is fully {P5,C6}-decomposable
Abstract
Let $P_{k+1}$ denote a path of length $k$, $C_{\ell}$ denote a cycle of length $\ell$, and $K_{n}(\lambda)$ denote the complete multigraph on $n$ vertices in which every edge is taken $\lambda$ times. In this paper, we have obtained the necessary conditions for a $\{P_{k+1}, C_{\ell}\}$-decomposition of $K_{n}(\lambda)$ and proved that the necessary conditions are also sufficient when $k=4$ and $\ell=6$.
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