Anti-Ramsey properties of random graphs

We call a coloring of the edge set of a graph G a b-bounded coloring if no color is used more than b times. We say that a subset of the edges of G is rainbow if each edge is of a different color. A graph has property A(b, H) if every b-bounded coloring of its edges has a rainbow copy of H. We estimate the threshold for the random graph Gn,p to have property A(b, H).

• Type: Journal
• Year: 2010
• Where: JCT
• Authors: Tom Bohman, Alan M. Frieze, Oleg Pikhurko, Clifford D. Smyth
• Keywords: Color, Edge, JCT 2010, Rainbow