Minimal colorings for properly colored subgraphs in complete graphs

Abstract

Let pr(K n , G) be the maximum number of colors in an edge-coloring of K n with no properly colored copy of G. In this paper, we show that pr, where G ′ = {G − M : M is a matching of G}. Furthermore, we determine the value of pr(K n , P l ) for l ≥ 27 and n ≥ 2l 3 and the exact value of pr(K n , G), where G is C 5 , C 6 and K − 4 , respectively. Also, we give an upper bound and a lower bound of pr(K n , K 2,3 ).