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 ...
Minimum numbers of monochromatic triangles in line $2$-colorings of $v_{3}$ configurations of points and lines This paper begins by exploring some old and new results about minimum numbers of monochromatic triangles in 2 -colorings of complete graphs, both in the di... J Bishop,R Kuss,B...
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 ...
Furthermore, we show that an edge-colored graph G contains at least k rainbow triangles if ∑v∈V(G)dGc(v)≥n+12+k?1 where dGc(v) denotes the number of distinct colors incident to a vertex v.Finally we characterize the edge-colored graphs without a rainbow clique of size at least ...
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...
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 ...
In this paper, the existence of rainbow triangles in edge-colored Kneser graphs is studied. We give bounds for the anti-Ramsey number of triangles in Kneser graphs. Also, the anti-Ramsey number of triangles with an pendant edge is studied and the bounds are equal to bounds for triangles. ...
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 ...
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...