1. Rainbow triangles in edge-colored graphs.
- Author
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Li, Binlong, Ning, Bo, Xu, Chuandong, and Zhang, Shenggui
- Subjects
- *
TRIANGLES , *GRAPH coloring , *GRAPH theory , *NUMBER theory , *PATHS & cycles in graph theory , *EXISTENCE theorems - Abstract
Abstract: Let be an edge-colored graph. The color degree of a vertex of , is defined as the number of colors of the edges incident to . The color number of is defined as the number of colors of the edges in . A rainbow triangle is one in which every pair of edges have distinct colors. In this paper we give some sufficient conditions for the existence of rainbow triangles in edge-colored graphs in terms of color degree, color number and edge number. As a corollary, a conjecture proposed by Li and Wang [H. Li and G. Wang, Color degree and heterochromatic cycles in edge-colored graphs, European J. Combin. 33 (2012) 1958–1964] is confirmed. [Copyright &y& Elsevier]
- Published
- 2014
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