2014/07/18 by Oliver Schaudt, Schaudt, Oliver, Maya Stein +1
Computer Science · Engineering · Mathematics · #05C38 #05C55 #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Limits and Structures in Graph Theory #cs.DM #graph theory and CDMA systems #math.CO #msc:05C38 #msc:05C55
paper · pdf · doi:10.48550/arxiv.1407.5083
openalex publication_date 2014/07/18 · arxiv created 2014/10/07 · arxiv updated 2014/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. We prove this under the necessary assumption 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.