August 11, 2025

New bound on the odd chromatic number of planar graphs with maximum degree at most 4

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Authors

VCVinícius de Souza CarvalhoUniversidade Federal do ABC CLCarla Négri LintzmayerUniversidade Federal do ABC MSMaycon SambinelliUniversidade Federal do ABC

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Implication

This research shows the odd chromatic number is at most 7 in planar graphs with a maximum degree of 4, suggesting tighter limits than previously known.

Key Points

Every planar graph with a maximum degree of 4 has an odd chromatic number less than or equal to 7, confirming a new upper limit.
The research demonstrates that this upper bound is an improvement over the previous best known limit of 8 for planar graphs.
Using principles of proper vertex coloring, the study offers significant insights into the properties of planar graphs and their colorings.
The findings highlight the conjectured relationship between maximum degree and chromatic numbers in planar graph theory.

Cite This Study

Carvalho et al. (2025) studied this question.

synapsesocial.com/papers/68a35ee30a429f7973327ace https://doi.org/10.5753/etc.2025.9399

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Implication

This research shows the odd chromatic number is at most 7 in planar graphs with a maximum degree of 4, suggesting tighter limits than previously known.

New bound on the odd chromatic number of planar graphs with maximum degree at most 4

Discussion

Member takes

Implication

Key Points

Cite This Study

New bound on the odd chromatic number of planar graphs with maximum degree at most 4

Discussion

Member takes

Implication

Key Points

Cite This Study

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