Abstract
The anti-Ramsey number ARG,H is the maximum number of colors in an edge-coloring of G such that G contains no rainbow subgraphs isomorphic to H. In this paper, we discuss the anti-Ramsey numbers ARKp1,p2,…,pk,Tn, ARKp1,p2,…,pk,ℳ, and ARKp1,p2,…,pk,C of Kp1,p2,…,pk, where Tn,ℳ, and C denote the family of all spanning trees, the family of all perfect matchings, and the family of all Hamilton cycles in Kp1,p2,…,pk, respectively.
Highlights
Let G be a graph, a k-edge-coloring of a graph G (V, E) is a mapping c: E ⟶ C, where C is a set of colors, namely, C {1, 2, . . . , k} [1]
Rainbow coloring of graphs has its application in practice. It comes from the secure communication of information between agencies of government. e anti-Ramsey number was introduced by Erdo€s, Simonovits, and So s in 1973 [2]
It has been shown that the anti-Ramsey number AR(G, H) is closely related to
Summary
E anti-Ramsey problems for rainbow matchings, cycles, and trees in complete bipartite graphs have been studied in [9,10,11]. It is natural to consider that the anti-Ramsey problems for rainbow matchings, cycles, and trees in complete k-partite graphs. Ramsey numbers for spanning trees, perfect matchings, and Hamilton cycles in complete k-partite graphs.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
