Edge-Colorings of Complete Graphs that Avoid Polychromatic Trees

Given a positive integer n and a family F of graphs, let R(n, F) denote the maximum number of colors in an edge-coloring of Kn such that no subgraph of Kn belonging to F has distinct colors on its edges. We determine R(n, Tk), where Tk is the family of trees with k edges. We derive general bounds for R(n, T), where T is an arbitrary tree with k edges. Finally, we present a single tree T with k edges such that R(n, T) is nearly as small as R(n, Tk).

• Type: Journal
• Year: 2002
• Where: ENDM
• Authors: Tao Jiang, Douglas B. West
• Keywords: ENDM 2002, General Bounds, Maximum Number, Positive Integer