Monochromatic Loose-Cycle Partitions in Hypergraphs
In this paper we study the monochromatic loose-cycle partition problem for non-complete hypergraphs. Our main result is that in any $r$-coloring of a $k$-uniform hypergraph with independence number $\alpha$ there is a partition of the vertex set into monochromatic loose cycles such that their number depends only on $r$, $k$ and $\alpha$. We also give an extension of the following result of Pósa to hypergraphs: the vertex set of every graph $G$ can be partitioned into at most $\alpha(G)$ cycles, edges and vertices.
2013 ◽
Vol 12
(04)
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pp. 1250199
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2012 ◽
Vol 12
(03)
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pp. 1250179
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2017 ◽
Vol 27
(4)
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pp. 531-538
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