Pokrovskiy, Alexey (2013) Partitioning edge-coloured complete graphs into monochromatic cycles. Electronic Notes in Discrete Mathematics, 43 . pp. 311-317. ISSN 1571-0653
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. |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Date Deposited: | 16 Sep 2013 08:51 |
| URL: | http://eprints.lse.ac.uk/52600/ |
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