Rainbow triangles in edge-colored graphs

Let GG be an edge-colored graph. The color degree of a vertex vv of GG, is defined as the number of colors of the edges incident to vv. The color number of GG is defined as the number of colors of the edges in GG. 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.