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arXiv · 1410.0445

Multicolored Isomorphic Spanning Trees in Complete Graphs

Hung-Lin Fu·Yuan-Hsun Lo
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Abstract

In this paper, we first prove that if the edges of $K_{2m}$ are properly colored by $2m-1$ colors in such a way that any two colors induce a 2-factor of which each component is a 4-cycle, then $K_{2m}$ can be decomposed into $m$ isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2$m-$1)-edge-colored $K_{2m}$ for $m\geq 14$.

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Hung-Lin Fu, Yuan-Hsun Lo. 2014-10-02. Multicolored Isomorphic Spanning Trees in Complete Graphs. https://arxiv.org/abs/1410.0445

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