Regular Bipartite Graphs Are Antimagic

A labeling of a graph G is a bijection from E(G) to the set {1, 2, ... , vertical bar E(G)vertical bar}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every connected graph other than K-2 is antimagic. In this article, we show that every regular bipartite graph (with degree at least 2) is antimagic. Our technique relies heavily on the Marriage Theorem. (c) 2008 Wiley Periodicals Inc. J Graph Theory 60: 173-192, 2009