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Proof of a local antimagic conjecture
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Haslegrave, John (2018) Proof of a local antimagic conjecture. Discrete Mathematics and Theoretical Computer Science, 20 (1). ISSN 1365-8050.
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Official URL: https://dmtcs.episciences.org/4550
Abstract
An antimagic labelling of a graph G is a bijection f : E ( G ) →{ 1 , . . . , | E ( G ) |} such that the sums S v = ∑ e 3 v f ( e ) distinguish all vertices v. A well-known conjecture of Hartsfield and Ringel (1994) is that every connected graph other than K 2 admits an antimagic labelling. Recently, two sets of authors (Arumugam, Premalatha, Bača & Semaničová-Feňovčıková (2017) and Bensmail, Senhaji & Szabo Lyngsie (2017)) independently introduced the weaker notion of a local antimagic labelling , where only adjacent vertices must be distinguished. Both sets of authors conjectured that any connected graph other than K 2 admits a local antimagic labelling. We prove this latter conjecture using the probabilistic method. Thus the parameter of local antimagic chromatic number, introduced by Arumugam et al., is well-defined for every connected graph other than K 2.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Graph theory | ||||||
| Journal or Publication Title: | Discrete Mathematics and Theoretical Computer Science | ||||||
| Publisher: | Discrete Mathematics and Theoretical Computer Science | ||||||
| ISSN: | 1365-8050 | ||||||
| Official Date: | 4 June 2018 | ||||||
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| Volume: | 20 | ||||||
| Number: | 1 | ||||||
| Number of Pages: | 14 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 4 June 2018 | ||||||
| Date of first compliant Open Access: | 4 June 2018 | ||||||
| RIOXX Funder/Project Grant: |
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