Decomposing graphs into a constant number of locally irregular subgraphs

DOI10.1016/J.EJC.2016.09.011zbMath1348.05161DBLPjournals/ejc/BensmailMT17arXiv1604.00235OpenAlexW2963794656WikidataQ56926485 ScholiaQ56926485MaRDI QIDQ338587

Carsten Thomassen, Julien Bensmail, Martin Merker

Publication date: 7 November 2016

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00235

zbMATH Keywords

graph decomposition1-2-3 conjectureedge set partitionlocally irregular graph

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (18)

A Note on the Locally Irregular Edge Colorings of Cacti ⋮ A note on the weak \((2,2)\)-conjecture ⋮ New bounds for locally irregular chromatic index of bipartite and subcubic graphs ⋮ On locally irregular decompositions of subcubic graphs ⋮ Decomposing degenerate graphs into locally irregular subgraphs ⋮ On the standard \((2,2)\)-conjecture ⋮ A generalization of Faudree–Lehel conjecture holds almost surely for random graphs ⋮ Locally irregular edge-coloring of subcubic graphs ⋮ Modulo orientations with bounded out-degrees ⋮ Asymptotic confirmation of the Faudree–Lehel conjecture on irregularity strength for all but extreme degrees ⋮ Local irregularity conjecture for 2-multigraphs versus cacti ⋮ On decomposing multigraphs into locally irregular submultigraphs ⋮ Local irregularity conjecture vs. cacti ⋮ Algorithmic complexity of weakly semiregular partitioning and the representation number ⋮ Decomposability of graphs into subgraphs fulfilling the 1-2-3 conjecture ⋮ Decomposing split graphs into locally irregular graphs ⋮ Decomposing split graphs into locally irregular graphs ⋮ Graph classes with locally irregular chromatic index at most 4

Cites Work

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• On decomposing graphs of large minimum degree into locally irregular subgraphs
• The 3-flow conjecture, factors modulo \(k\), and the 1-2-3-conjecture
• Graph factors modulo \(k\)
• The weak 3-flow conjecture and the weak circular flow conjecture
• Nowhere-zero 3-flows and modulo \(k\)-orientations
• Vertex-coloring edge-weightings: towards the 1-2-3-conjecture
• Edge weights and vertex colours
• On the complexity of determining the irregular chromatic index of a graph
• On decomposing regular graphs into locally irregular subgraphs
• Bounding the weight choosability number of a graph

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