Anti-Ramsey Numbers in Complete k-Partite Graphs

الملخص EN

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.