A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper,we study the proper edgecolorings of the complete bipartite graph Km,n which forbid multicolored cycles. Mainly,we prove that(1)for any integer k ≥ 2, if n ≥ 5k - 6, then any properly n-edge-colored Kk,n contains a multicolored C 2k,and(2)determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored C6.
|Number of pages||8|
|State||Published - 1 Mar 2013|
- Complete bipartite graph
- Multicolored cycle