Pokrovskiy, Alexey (2011) Partitioning 3-coloured complete graphs into three monochromatic paths. Electronic notes in discrete mathematics, 38 . pp. 717-722. ISSN 1571-0653
In this paper we show that in any edge-colouring of the complete graph by three colours, it is possible to cover all the vertices by three disjoint monochromatic paths. This solves a particular case of a conjecture of Gyárfás. As an intermediate result, we show that in any edge colouring of the complete graph by two colours, it is possible to cover all the vertices by a monochromatic path and a disjoint monochromatic balanced complete bipartite graph.
|Additional Information:||© 2011 Elsevier|
|Uncontrolled Keywords:||ISI, edge colourings, monochromatic partitions|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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