What does this research mean for the field?

For any graph that is either K3,3-minor-free or K5-minor-free, a specific mathematical bound on its weak degeneracy holds. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish upper bounds on the weak degeneracy parameter for graphs excluding complete or complete bipartite minors.

August 30, 2026Discrete Mathematics Algorithms and Applications

A note on weak degeneracy of K 3,3 -minor-free graphs and K 5 -minor-free graphs

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Authors

TCTingting Chen MHMiaomiao Han

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Implication

Theoretical analysis establishes upper bounds on weak degeneracy in K3,3-minor-free and K5-minor-free graphs, highlighting direct constraints on coloring parameters like DP-chromatic numbers.

Key Points

To establish upper bounds on the weak degeneracy parameter for graphs excluding complete or complete bipartite minors.
Conducted structural graph-theoretic proofs analyzing graph classes that exclude either K3,3 or K5 minors.
Demonstrated a strict upper bound on the weak degeneracy of any graph free of K3,3 or K5 minors.
Provided corresponding upper bounds on related coloring parameters, including the DP-chromatic number and Alon-Tarsi number.

Cite This Study

Chen et al. (2026) studied this question.

synapsesocial.com/papers/6a93f1396c1a8fb52e79e06d https://doi.org/10.1142/s1793830926500862

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August 30, 2026Discrete Mathematics Algorithms and Applications

A note on weak degeneracy of K 3,3 -minor-free graphs and K 5 -minor-free graphs

View Full Paper

Ask AI

Bookmark

Authors

TCTingting Chen MHMiaomiao Han

Discussion

Member takes

Implication

Theoretical analysis establishes upper bounds on weak degeneracy in K3,3-minor-free and K5-minor-free graphs, highlighting direct constraints on coloring parameters like DP-chromatic numbers.

Key Points

To establish upper bounds on the weak degeneracy parameter for graphs excluding complete or complete bipartite minors.
Conducted structural graph-theoretic proofs analyzing graph classes that exclude either K3,3 or K5 minors.
Demonstrated a strict upper bound on the weak degeneracy of any graph free of K3,3 or K5 minors.
Provided corresponding upper bounds on related coloring parameters, including the DP-chromatic number and Alon-Tarsi number.

Cite This Study

Chen et al. (2026) studied this question.

synapsesocial.com/papers/6a93f1396c1a8fb52e79e06d https://doi.org/10.1142/s1793830926500862

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