A complete bipartite graph without properly colored cycles of length four | Zendy

Čada Roman | Zendy; Ozeki Kenta | Zendy; Yoshimoto Kiyoshi | Zendy

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A complete bipartite graph without properly colored cycles of length four

Author(s) -

Čada Roman,

Ozeki Kenta,

Yoshimoto Kiyoshi

Publication year - 2020

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22480

Subject(s) - combinatorics , mathematics , bipartite graph , corollary , complete bipartite graph , robertson–seymour theorem , monochromatic color , complete graph , discrete mathematics , graph factorization , colored , edge coloring , graph , 1 planar graph , chordal graph , graph power , line graph , materials science , composite material , botany , biology

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 C 4 . 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 C 4 . Our decomposition gives a corollary on the existence of a monochromatic star with almost sharp bound.

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