In this study we consider a Ramsey property of random d-regular graphs, g(n, d). Let r ≥ 2 be fixed. Then w.h.p. the edges of g(n, 2r) can be colored such that every monochromatic component has order o (n). On the other hand, there exists a constant γ > 0 such that w.h.p., every r-coloring of the edges of g(n, 2r + 1) must contain a monochromatic cycle of length at least γn. We prove an analogous result for random k -out graphs.
|Number of pages||9|
|Journal||Journal of Graph Theory|
|State||Published - 1 Mar 2020|
- monochromatic components
- random k-out graphs
- random regular graphs