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October 12, 2025Open Access

Planar Graphs with Ore-degree at Most seven is strongly 13-edge-colorable

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Authors

SNS. NelsonGYGexin Yu

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Overview

This research demonstrates that planar graphs with Ore-degree up to 7 have strong chromatic index of 13, suggesting improved edge-coloring methods.

Key Points

  • Every planar graph with Ore-degree at most 7 has a strong chromatic index of 13, confirming an existing conjecture.
  • The strong chromatic index defines the minimum colors needed where each color forms an induced matching.
  • A discharging method coupled with combinatorial nullstellensatz is utilized to demonstrate reducible configurations.
  • An algorithm is provided for utilizing combinatorial nullstellensatz to extract coefficients from large polynomials.

Cite This Study

Nelson et al. (2025) studied this question.

synapsesocial.com/papers/68ec1be02b8fa9b2b78ad272https://doi.org/10.48550/arxiv.2509.06808
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