Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653180 | European Journal of Combinatorics | 2017 | 13 Pages |
Abstract
We show that for any 2-local colouring of the edges of the balanced complete bipartite graph Kn,nKn,n, its vertices can be covered with at most 3 disjoint monochromatic paths. And, we can cover almost all vertices of any complete or balanced complete bipartite rr-locally coloured graph with O(r2)O(r2) disjoint monochromatic cycles. We also determine the 2-local bipartite Ramsey number of a path almost exactly: Every 2-local colouring of the edges of Kn,nKn,n contains a monochromatic path on nn vertices.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Richard Lang, Maya Stein,