Antimagic labelings of regular bipartite graphs: An application of the Marriage Theorem

Details Antimagic labelings of regular bipartite graphs: An application of the Marriage Theorem Antimagic labelings of regular bipartite graphs: An application of the Marriage Theorem

2007-08-21

arxiv.org/abs/0708.2776v1

Journal of Graph Theory. Vol. 60, March 2009, pp. 173-182

Mathematics

Combinatorics

9 pages

Scientific paper

A labeling of a graph is a bijection from $E(G)$ to the set $\{1, 2,..., |E(G)|\}$. A labeling is \textit{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, Ringel conjectured that every connected graph other than $K_2$ is antimagic. In this paper, we show that every regular bipartite graph (with degree at least 2) is antimagic. Our technique relies heavily on the Marriage Theorem.

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