Universität zu Köln

Schaudt, Oliver and Stein, Maya (2019). Partitioning two-coloured complete multipartite graphs into monochromatic paths and cycles. J. Graph Theory, 91 (2). S. 122 - 148. HOBOKEN: WILEY. ISSN 1097-0118

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Abstract

We show that any complete k-partite graph G on n vertices, with k >= 3, whose edges are two-coloured, can be covered with two vertex-disjoint monochromatic paths of distinct colours, given that the largest partition class of G contains at most n/2 vertices. This extends known results for complete and complete bipartite graphs. Secondly, we show that in the same situation, all but o(n) vertices of the graph can be covered with two vertex-disjoint monochromatic cycles of distinct colours, if colourings close to a split colouring are excluded. From this we derive that the whole graph, if large enough, may be covered with 14 vertex-disjoint monochromatic cycles.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schaudt, Oliver UNSPECIFIED UNSPECIFIED UNSPECIFIED Stein, Maya UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-138405
DOI:	10.1002/jgt.22424
Journal or Publication Title:	J. Graph Theory
Volume:	91
Number:	2
Page Range:	S. 122 - 148
Date:	2019
Publisher:	WILEY
Place of Publication:	HOBOKEN
ISSN:	1097-0118
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language VERTEX COVERINGS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13840