Anti-Ramsey theory on complete bipartite graphs. Issue 3 (1st September 2020) - Cho, Stephan; Cummings, Jay; Defant, Colin; Sonneborn, Claire
Abstract: We consider quadruples of positive integers ( a, b, m, n ) with a ≤ b and m ≤ n such that every proper edge-coloring of the complete bipartite graph K m, n contains a rainbow K a, b subgraph. We show that every such quadruple with m ≥ a and n > ( a 2 − a + 1 ) ( b − 1 ) satisfies this property and find an infinite sequence where this bound is sharp. We also define and compute some new anti-Ramsey numbers.