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arbitrarily decomposable into closed trails |
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Abstract: In the paper it is proved that any complete tripartite graph $K_{r,r,r}$, where $r=5 \cdot 2^n$ and $n$ is a nonnegative integer, has the following property: Whenever $(l_1, \dots ,l_p)$ is a sequence of integers $\geq 3$ adding up to $|E(K_{r,r,r})|$, there is a sequence $(T_1, \dots ,T_p)$ of edge-disjoint closed trails in $K_{r,r,r}$ such that $T_i$ is of length $l_i$, $i=1, \dots ,p$. Contact the authors: hornak@science.upjs.sk, kockova@science.upjs.sk Download PDF version of the preprint. |