Partitioning Complete Bipartite Graphs by Monochromatic Cycles
Copyright policy )Partitioning Complete Bipartite Graphs by Monochromatic Cycles
For every positive integer \(r\) there exists a constant \(C_r\) depending only on \(r\) such that for every colouring of the edges of the complete bipartite graph \(K^{n,n}\) with \(r\) colours, there exists a set of at most \(C_r\) monochromatic cycles whose vertex sets partition the vertex set of \(K^{n,n}\). This answers a question raised by \textit{P. Erdös}, \textit{A. Gyárfás} and \textit{L. Pyber} [J. Comb. Theory, Ser. B 51, No. 1, 90-95 (1991; Zbl 0766.05062)].
- University of Waterloo Canada
colouring, monochromatic cycles, Eulerian and Hamiltonian graphs, Coloring of graphs and hypergraphs, Computational Theory and Mathematics, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), complete bipartite graph, Discrete Mathematics and Combinatorics, Paths and cycles, partition, Theoretical Computer Science
colouring, monochromatic cycles, Eulerian and Hamiltonian graphs, Coloring of graphs and hypergraphs, Computational Theory and Mathematics, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), complete bipartite graph, Discrete Mathematics and Combinatorics, Paths and cycles, partition, Theoretical Computer Science
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