Vertex covers by monochromatic pieces - A survey of results and problems

Abstract

This survey is devoted to problems and results concerning covering the vertices of edge colored graphs or hypergraphs with monochromatic paths, cycles and other objects. It is an expanded version of the talk with the same title at the Seventh Cracow Conference on Graph Theory, held in Rytro in September 14-19, 2014.

Discrete Mathematics, 2015

References in corpus (5)

• Partitioning 2-edge-colored graphs by monochromatic paths and cycles
• Monochromatic cycle partitions in local edge colourings
• Calculating Ramsey numbers by partitioning coloured graphs
• Local colourings and monochromatic partitions in complete bipartite graphs
• Partitioning two-coloured complete multipartite graphs into monochromatic paths and cycles

Cited by in corpus (9)

• Partitioning edge-coloured hypergraphs into few monochromatic tight cycles
• Monochromatic tree covers and Ramsey numbers for set-coloured graphs
• Monochromatic cycle partitions in random graphs
• Almost partitioning 2-coloured complete 3-uniform hypergraphs into two monochromatic tight or loose cycles
• Partitioning $2$-coloured complete $k$-uniform hypergraphs into monochromatic $\ell$-cycles
• Tiling with monochromatic bipartite graphs of bounded maximum degree
• Monochromatic loose path partitions in k-uniform hypergraphs
• Powers of paths and cycles in tournaments
• Partitioning a 2-edge-coloured graph of minimum degree $2n/3+o(n)$ into three monochromatic cycles