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A note on decomposing graphs to locally almost irregular subgraphs

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  • Przybyło, Jakub

Abstract

We consider a concept related with decompositions of graphs to locally irregular subgraphs and the notion of almost irregular subgraphs, introduced recently by Alon and Wei. We say that a graph is locally almost irregular if its every vertex has at most one neighbour with the same degree as itself. We conjecture that any graph can be edge decomposed to two locally almost irregular subgraphs, and we prove a relaxation of this supposition, where we admit for every vertex v more than one, yet finitely bounded number of neighbours with the same degree as v. In particular we show it suffices to allow 7 such neighbours in the case of regular graph, and no more than 48 in general.

Suggested Citation

  • Przybyło, Jakub, 2024. "A note on decomposing graphs to locally almost irregular subgraphs," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    • Handle: RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000560
    DOI: 10.1016/j.amc.2024.128584
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    References listed on IDEAS

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    1. Jelena Sedlar & Riste Škrekovski, 2021. "Remarks on the Local Irregularity Conjecture," Mathematics, MDPI, vol. 9(24), pages 1-10, December.
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