A complete bipartite graph without properly colored cycles of length four.

A subgraph of an edge‐colored graph is said to be properly colored, or shortly PC, if any two adjacent edges have different colors. Fujita, Li, and Zhang gave a decomposition theorem for edge‐colorings of complete bipartite graphs without PC C4. However, their decomposition just focuses on a local structure. In this paper, we give a new and global decomposition theorem for edge‐colorings of complete bipartite graphs without PC C4. Our decomposition gives a corollary on the existence of a monochromatic star with almost sharp bound. [ABSTRACT FROM AUTHOR]