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A Solution to the 1-2-3 Conjecture

Combinatorics 2024-01-30 v4
Authors: Ralph Keusch
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Abstract

We show that for every graph without isolated edge, the edges can be assigned weights from {1,2,3} so that no two neighbors receive the same sum of incident edge weights. This solves a conjecture of Karo\'{n}ski, Luczak, and Thomason from 2004.

Keywords

graph theory hadwiger conjecture random graphs

Cite

@article{arxiv.2303.02611,
  title  = {A Solution to the 1-2-3 Conjecture},
  author = {Ralph Keusch},
  journal= {arXiv preprint arXiv:2303.02611},
  year   = {2024}
}

Comments

16 pages

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