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PreprintCC BY 4.0arXiv

An 18-colour bound for locally irregular decompositions

  • Carla Negri Lintzmayer
  • Guilherme Oliveira Mota
  • Maycon Sambinelli
  • Vinicius Fernandes dos Santos
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Abstract

A graph is locally irregular if adjacent vertices have distinct degrees. A graph G is decomposable if its edge set can be decomposed into locally irregular graphs, and its locally irregular chromatic index lir(G) is the least number of graphs in such a decomposition. We prove that lir(G) <= 18 for every decomposable graph G, improving the previous bound of 220.

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Cite

BibTeXRIS
BibTeX
@misc{lintzmayer202618colour,
  title = {{An 18-colour bound for locally irregular decompositions}},
  author = {Carla Negri Lintzmayer and Guilherme Oliveira Mota and Maycon Sambinelli and Vinicius Fernandes dos Santos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09355},
  eprint = {2609.09355},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09355},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An 18-colour bound for locally irregular decompositions
AU  - Carla Negri Lintzmayer
AU  - Guilherme Oliveira Mota
AU  - Maycon Sambinelli
AU  - Vinicius Fernandes dos Santos
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09355
UR  - https://arxiv.org/abs/2609.09355
AB  - A graph is locally irregular if adjacent vertices have distinct degrees. A graph G is decomposable if its edge set can be decomposed into locally irregular graphs, and its locally irregular chromatic index lir(G) is the least number of graphs in such a decomposition. We prove that lir(G) <= 18 for every decomposable graph G, improving the previous bound of 220.
ER  -