منابع مشابه
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 α there is a partition of the vertex set into monochromatic loose cycles such that their number depends only on r, k and α. We also give an extension of the following result of Pósa to hypergraphs: the v...
متن کاملImproved monochromatic loose cycle partitions in hypergraphs
Improving our earlier result we show that every large enough complete kuniform r-colored hypergraph can be partitioned into at most 50rk log (rk) vertex disjoint monochromatic loose cycles. The proof is using the strong hypergraph Regularity Lemma due to Rödl and Schacht and the new, powerful hypergraph Blow-up Lemma of Keevash. 1 Monochromatic cycle partitions Assume first that Kn is a complet...
متن کاملMonochromatic cycle partitions of edge-colored graphs
In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G)= . Generalizing a classical conjecture of Erd” os, Gyárfás and Pyber, we conjecture that if we r -color the edges of a graph G with (G)= , then the vertex set of G can be partitioned into at most r vertex disjoint monochromatic cycles. In the direct...
متن کاملMonochromatic Path and Cycle Partitions in Hypergraphs
Here we address the problem to partition edge colored hypergraphs by monochromatic paths and cycles generalizing a well-known similar problem for graphs. We show that r-colored r-uniform complete hypergraphs can be partitioned into monochromatic Berge-paths of distinct colors. Also, apart from 2k − 5 vertices, 2-colored k-uniform hypergraphs can be partitioned into two monochromatic loose paths...
متن کاملMonochromatic Cycle Partitions in Local Edge Colorings
An edge colouring of a graph is said to be an r-local colouring if the edges incident to any vertex are coloured with at most r colours. Generalising a result of Bessy–Thomassé and others, we prove that the vertex set of any 2-locally coloured complete graph may be partitioned into two disjoint monochromatic cycles of different colours. Moreover, for any natural number r, we show that the verte...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.08.009