1 research outputs found
Avoiding rainbow induced subgraphs in vertex-colorings
For a fixed graph on vertices, and a graph on at least
vertices, we write if in any vertex-coloring of with
colors, there is an induced subgraph isomorphic to whose vertices have
distinct colors. In other words, if then a totally
multicolored induced copy of is unavoidable in any vertex-coloring of
with colors. In this paper, we show that, with a few notable exceptions,
for any graph on vertices and for any graph which is not isomorphic
to , . We explicitly describe all exceptional cases.
This determines the induced vertex-anti-Ramsey number for all graphs and shows
that totally multicolored induced subgraphs are, in most cases, easily
avoidable.Comment: 23 pages, 3 figure