Rainbow matchings in edge-colored complete split graphs

Rainbow number of matchings in planar graphs

Improved bounds for rainbow numbers of matchings in plane triangulations

Given a graph G, the anti-Ramsey number $$AR(K_n,G)$$
 is defined to be the maximum number of colors in an edge-coloring of $$K_n$$
 which does not contain any rainbow G (i.e., all the edges of G have distinct colors). The anti-Ramsey number was introduced by Erdős et al. (Infinite and finite sets, pp 657–665, 1973) and so far it has been determined for several special graph classes. Another related interesting problem posed by Erdős et al. is the uniqueness of the extremal coloring for the anti-Ramsey number. Contrary to the anti-Ramsey number, there are few results about the extremal coloring. In this paper, we show the uniqueness of such extremal coloring for the anti-Ramsey number of matchings in the complete graph.

Extremal coloring for the anti-Ramsey problem of matchings in complete graphs

Anti-Ramsey number of matchings in a hypergraph

Let &#x1d4a2; be a family of graphs. The anti-Ramsey number AR(G,&#x1d4a2;) for &#x1d4a2; in the graph G is the maximum number of colors in an edge coloring of G that does not have any rainbow copy of any graph in &#x1d4a2;. In this paper, we consider the anti-Ramsey number for matchings in regular bipartite graphs and determine its value under several conditions.

Anti-Ramsey numbers for matchings in regular bipartite graphs

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Anti-Ramsey numbers for matchings in regular bipartite graphs