The \(1,2,3\)-conjecture and \(1,2\)-conjecture for sparse graphs

DOI10.7151/dmgt.1768zbMath1303.05172arXiv1303.3198OpenAlexW1999442360WikidataQ123198810 ScholiaQ123198810MaRDI QIDQ472134

Sogol Jahanbekam, Daniel W. Cranston, Douglas B. West

Publication date: 18 November 2014

Published in: Discussiones Mathematicae. Graph Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.3198

zbMATH Keywords

discharging method\(1,2,3\)-conjecture\(1,2\)-conjecturereducible configuration

Mathematics Subject Classification ID

Structural characterization of families of graphs (05C75) Coloring of graphs and hypergraphs (05C15) Graph labelling (graceful graphs, bandwidth, etc.) (05C78) Signed and weighted graphs (05C22) Density (toughness, etc.) (05C42)

Related Items (5)

Total weight choosability of graphs with bounded maximum average degree ⋮ Graphs with maximum average degree less than \(\frac{11}{4}\) are \((1, 3)\)-choosable ⋮ On the semi-proper orientations of graphs ⋮ An introduction to the discharging method via graph coloring ⋮ On weight choosabilities of graphs with bounded maximum average degree

Cites Work

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• Every graph is \((2,3)\)-choosable
• Vertex-coloring edge-weightings: towards the 1-2-3-conjecture
• On vertex-coloring 13-edge-weighting
• Edge weights and vertex colours
• Vertex-colouring edge-weightings
• Degree constrained subgraphs
• Bounding the weight choosability number of a graph
• Weight choosability of graphs
• Combinatorial Nullstellensatz
• Total weight choosability of graphs

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