Geodesic
Rainbow disjoint union of clique and matching in edge-colored complete graph
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 953-970

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Given an edge-coloring of a graph G, G is said to be rainbow if any two edges of G receive different colors. The anti-Ramsey number AR(G,H) is defined to be the maximum integer k such that there exists a k-edge-coloring of G avoiding rainbow copies of H. The anti-Ramsey number for graphs, especially matchings, have been studied in several graph classes. Gilboa and Roditty focused on the anti-Ramsey number of graphs with small components, especially including a matching. In this paper, we continue the work in this direct and determine the exact value of the anti-Ramsey number of K_4∪ tP_2 in complete graphs. Also, we improve the bound and obtain the exact value of AR(K_n,C_3∪ tP_2) for all n≥ 2t+3.
Keywords: rainbow matching, anti-Ramsey number, clique 
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Jin, Zemin; Gu, Junqi. Rainbow disjoint union of clique and matching in edge-colored complete graph. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 953-970. http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a7/