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Partitioning edge-coloured complete graphs into monochromatic cycles

Pokrovskiy, Alexey (2013) Partitioning edge-coloured complete graphs into monochromatic cycles. Electronic Notes in Discrete Mathematics, 43. pp. 311-317. ISSN 1571-0653

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Identification Number: 10.1016/j.endm.2013.07.049

Abstract

A conjecture of Erdös, Gyárfás, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertex-disjoint monochromatic cycles. So far, this conjecture has been proven only for r=2. In this note we show that in fact this conjecture is false for all r⩾3. We also discuss some weakenings of this conjecture which may still be true.

Item Type: Article
Official URL: http://www.elsevier.com/locate/endm
Additional Information: © 2013 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 16 Sep 2013 08:51
Last Modified: 20 Jan 2020 05:04
URI: http://eprints.lse.ac.uk/id/eprint/52600

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