Bipartite rainbow numbers of matchings

Abstract

Given two graphs G

Rainbow generalizations of Ramsey theory - a dynamic survey

“…Others have studied rainbow matchings in bipartite graphs. Li, Tu and Jin [134] determined the anti-Ramsey number for matchings in complete bipartite graphs as follows. In looking at more sparse graphs, Li and Xu [133] determined the anti-Ramsey number for matchings in m-regular bipartite graphs of order 2n, denoted B n,m .…”

Anti-Ramsey problems in the generalized Petersen graphs for cycles

“…They presented a close relationship between the anti-Ramsey number and Turán number. Since then, plentiful results were researched for a variety of graphs H, including cycles [1,2,12,13,18,19], cliques [4,17], trees [9,11], and matchings [7,16]. Some other graphs were also considered as the host graphs in anti-Ramsey problems, such as hypergraphs [6], hypecubes [3], complete split graphs [5,14], and triangulations [8,10,15].…”

Anti-Ramsey Numbers in Complete k-Partite Graphs

“…e anti-Ramsey numbers for some other special graph classes in complete graphs have also been studied, including independent cycles [4], stars [5], spanning trees [6], and matchings [7,8]. e anti-Ramsey problems for rainbow matchings, cycles, and trees in complete bipartite graphs have been studied in [9][10][11]. Some other graphs were also considered as the host graphs in anti-Ramsey problems, such as hypergraphs [12], hypecubes [13], plane triangulations [14], and planar graphs [15].…”

“…In [9], it has been shown that AR(K m,n , kK 2 ) � m(k − 2) + 1, m ≥ n ≥ k ≥ 3, which is the maximum numbers of colors in an edge-coloring of K m,n that contains no rainbow kK 2 . Now, we consider the maximum numbers of colors in an edge-coloring of K p 1 ,p 2 ,...,p k not containing any rainbow perfect matching.…”