A solution to the 1-2-3 conjecture

DOI10.1016/j.jctb.2024.01.002arXiv2303.02611OpenAlexW4391247093MaRDI QIDQ6196158

Ralph Keusch

Publication date: 14 March 2024

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.02611

zbMATH Keywords

1-2-3 conjectureirregular graph labellingsweighted degrees

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Graph labelling (graceful graphs, bandwidth, etc.) (05C78) Signed and weighted graphs (05C22)

Cites Work

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• The 3-flow conjecture, factors modulo \(k\), and the 1-2-3-conjecture
• Every graph is \((2,3)\)-choosable
• Digraphs are 2-weight choosable
• Vertex-coloring edge-weightings of graphs
• Vertex-coloring edge-weightings: towards the 1-2-3-conjecture
• On vertex-coloring 13-edge-weighting
• Multi-set neighbor distinguishing 3-edge coloring
• A 1-2-3-4 result for the 1-2-3 conjecture in 5-regular graphs
• Edge weights and vertex colours
• Total weight choosability of graphs: towards the 1-2-3-conjecture
• Every nice graph is (1,5)-choosable
• The 1-2-3 conjecture almost holds for regular graphs
• From the 1-2-3 conjecture to the Riemann hypothesis
• Vertex-colouring edge-weightings
• Degree constrained subgraphs
• Vertex colouring edge partitions
• Weak and strong versions of the 1-2-3 conjecture for uniform hypergraphs
• Bounding the weight choosability number of a graph
• Weight choosability of graphs
• Combinatorial Nullstellensatz
• The 1‐2‐3‐conjecture holds for dense graphs
• The 1-2-3-Conjecture for Hypergraphs
• Total weight choosability of graphs
• Total weight choosability of graphs
• Vertex-coloring graphs with 4-edge-weightings

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