GENERALIZED RAINBOW CONNECTION OF GRAPH

Tóm tắt báo cáo

ABSTRACT: Let  be a nontrivial connected graph on which is defined an edge-coloring . A path  in  is called rainbow if each subgraph of length at most  is rainbow. The graph  is called rainbow connected if there is an edge-coloring such that every pair of distinct vertices of  is connected by  pairwise internally vertex-disjoint rainbow paths in . The rainbow connection number of graph , denoted by , is the smallest number of colors that are needed to make  rainbow connected. This report introduces connection problems and generalized rainbow connection of graphs. Then, we present the main results of .