WebRainbow spanning subgraphs of edge-colored complete graphs Sogol Jahanbekam∗and Douglas B. West† April 29, 2013 Abstract Consider edge-colorings of the complete graph … Web1.1 Rainbow cycles and paths Consider an edge colored graph G. A subgraph of G is called rainbow (or heterochromatic) if no two of its edges receive the same color. We are concerned with rainbow paths and, to a lesser extent, cycles in proper edge colorings of the complete graph Kn. Hahn conjectured that every proper edge coloring
Anti-Ramsey Number of Triangles in Complete Multipartite Graphs
WebSep 1, 2016 · A rainbow triangle in G is one in which all edges have distinct colors. In this paper, we first prove that an edge-colored graph on n vertices contains a rainbow triangle if the color degree sum of every two adjacent vertices is at least $$n+1$$n+1. WebCounting rainbow triangles in edge-colored graphs Xueliang Li∗, Bo Ning †, Yongtang Shi ‡, Shenggui Zhang § December 30, 2024 Abstract Let G be an edge-colored graph on n vertices. The minimum color degree of G, denoted by δc(G), is defined as the minimum number of colors assigned to the edges incident to a vertex in G. flyer lecture
Rainbow C3’s and C4’s in edge-colored graphs
WebDec 29, 2024 · As consequences, we prove counting results for rainbow triangles in edge-colored graphs. One main theorem states that the number of rainbow triangles in is at … WebRainbow C 3 ’s and C 4 ’s in edge-colored graphs October 2013 Authors: Hao li Beijing Institute of Technology Abstract Let G c be a graph of order n with an edge coloring C. A … WebIn graph theory, a path in an edge-colored graph is said to be rainbow if no color repeats on it. A graph is said to be rainbow-connected (or rainbow colored) if there is a rainbow path between each pair of its vertices.If there is a rainbow shortest path between each pair of vertices, the graph is said to be strongly rainbow-connected (or strongly rainbow colored). greening our city grant program