Caterpillars are Antimagic
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866910437160779776 |
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| author | Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín |
| author_facet | Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1812_06715 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Caterpillars are Antimagic Lozano, Antoni Mora, Mercè Seara, Carlos Tey, Joaquín Combinatorics 05C78 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. |
| title | Caterpillars are Antimagic |
| topic | Combinatorics 05C78 |
| url | https://arxiv.org/abs/1812.06715 |