We say that an edge-colored graph is rainbow if all its edges have different colors. In this paper, we consider vertex-disjoint rainbow triangles in edge-colored graphs. Li (2013) showed that if δc(G)≥(n+1)∕2
Rainbow triangles in edge-colored graphs 2014, European Journal of Combinatorics Show abstract Let G be an edge-colored graph. The color degree of a vertex v of G, is defined as the number of colors of the edges incident to v. The color number of G is defined as the number of colors...
In this paper, we consider color-degree conditions for the existence of rainbow triangles in edge-colored graphs. At first, we give a new proof for characterizing all extremal graphs G with \\(\\delta ^c(G)\\ge \\frac{n}{2}\\) that do not contain rainbow triangles, a known result...
Edge-colored graphsColor degreeRainbow trianglesLet G be an edge-colored graph and v a vertex of G. The color degree of v is the number of colors appearing on the edges incident to v. A rainbow triangle in G is one in which all edges have distinct colors. In this paper, we first ...
A rainbow triangle in Gis one in which all edges have distinct...doi:10.1007/s00373-016-1690-2Li, RuonanNing, BoZhang, ShengguiSpringer JapanGraphs & CombinatoricsR. Li, B. Ning and S. Zhang, Color degree sum conditions for rainbow triangles in edge-colored graphs, Graphs Combin., 32 ...
Erdos and Sos proposed the problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F(n) = F (a) + F(b) + F(c) + F(d) abc + abd + acd + bcd, where a + b + c + d = n and a, b, c...
In this paper, we first give a sharp upper bound for src(G) in terms of the number of edge-disjoint triangles in a graph G, and give a necessary and sufficient condition for the equality. We next investigate the graphs with large strong rainbow connection numbers. Chartrand et al. ...
edge‐colored graphrainbow trianglesA famous conjecture of Caccetta and Häggkvist is that in a digraph on n vertices and minimum outdegree at least n / r there is a directed cycle of length r or less. We consider the following generalization: in an undirected graph on n vertices, any ...
Rainbow triangles in edge-colored Kneser graphs 2020, Applied Mathematics and Computation Citation Excerpt : The authors [12,17,25,26] considered the anti-Ramsey number for matching in planar graphs. Recently, Jin et al. [18] determined the number for matchings in complete split graphs which co...
An edge-colored complete graph without rainbow triangles has very special structure. In 1967, Gallai in [4] first examined this structure under the guise of transitive orientations of graphs and it can also be traced back to the paper [2]. For this reason, an edge-coloring of a complete ...