2018/08/29 by Carl Bürger, Bürger, Carl, Max Pitz +1
Computer Science · Mathematics · #05C15 #05C38 #05C63 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1808.09836
openalex publication_date 2018/08/29 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
In 1978, Richard Rado showed that every edge-coloured complete graph of\ncountably infinite order can be partitioned into monochromatic paths of\ndifferent colours. He asked whether this remains true for uncountable complete\ngraphs and a notion of \generalised paths. In 2016, Daniel Soukup\nanswered this in the affirmative and conjectured that a similar result should\nhold for complete bipartite graphs with bipartition classes of the same\ninfinite cardinality, namely that every such graph edge-coloured with r\ncolours can be partitioned into 2r-1 monochromatic generalised paths with\neach colour being used at most twice.\n In the present paper, we give an affirmative answer to Soukup's conjecture.\n