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arXiv · 1812.06715

Caterpillars are Antimagic

Antoni Lozano·Mercè Mora·Carlos Seara·Joaquín Tey
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Abstract

An antimagic labeling of a graph $G$ is an injection from $E(G)$ to $\{1,2,\dots,|E(G)|\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $u$ is the sum of the labels assigned to edges incident to $u$. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than $K_2$ is antimagic and the conjecture remains open even for trees. Here we prove that caterpillars are antimagic by means of an $O(n \log n)$ algorithm.

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Antoni Lozano, Mercè Mora, Carlos Seara, Joaquín Tey. 2019-03-26. Caterpillars are Antimagic. https://doi.org/10.1007/s00009-020-01688-z

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