Abstract

AbstractWe study colorings of the edges of the complete graph . For some graph , we say that a coloring contains a rainbow , if there is an embedding of into , such that all edges of the embedded copy have pairwise distinct colors. The main emphasis of this paper is a classification of those forbidden rainbow graphs that force a low number of vertices of a high color degree, along with some specifications and more general information in certain cases. Those graphs turn out to be of two special types of trees of small diameter.

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