What question did this study set out to answer?

The study aims to determine the injective chromatic index for K4-minor free graphs with maximum degree at most 4.

February 12, 2026Graphs and CombinatoricsOpen Access

Injective Edge-Colorings of K₄-Minor Free Graphs

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Demonstrates an upper bound on injective chromatic index in K4-minor free graphs, suggesting improved color usage.

The study aims to determine the injective chromatic index for K4-minor free graphs with maximum degree at most 4.
Analyzed properties of K4-minor free graphs
Derived bounds on injective chromatic index based on treewidth
Applied results from existing literature on subcubic and planar graphs
Proved that every K4-minor free graph with maximum degree at most 4 has an injective chromatic index of at most 7.
Showed that this result improves previous linear bounds to a constant for K4-minor free graphs.

Yu et al. (2026) studied this question.

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