What does this research mean for the field?

Every simple cubic bipartite graph on at most 58 vertices contains a cycle of length 4, 8, or 16, establishing a new lower bound of 60 vertices for any cubic bipartite counterexample to the Erdős–Gyárfás conjecture. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine the minimum vertex count required for cubic bipartite graphs to serve as counterexamples to the Erdős–Gyárfás conjecture.

August 1, 2026Open Access

A 60-Vertex Lower Bound for Cubic Bipartite Counterexamples to the Erdős–Gyárfás Conjecture

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To determine the minimum vertex count required for cubic bipartite graphs to serve as counterexamples to the Erdős–Gyárfás conjecture.
Exact exhaustive computation of cubic bipartite graphs with up to 58 vertices.
Symmetric 3-uniform, 3-regular incidence structures are used for candidate encoding.
Implementations covering side sizes 7 through 29 and 9 through 29 are utilized.
Every cubic bipartite graph on at most 58 vertices contains cycles of length 4, 8, or 16.
Any cubic bipartite counterexample to the Erdős–Gyárfás conjecture has at least 60 vertices.
The lower bound for such counterexamples is raised from 30 to 60.

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Implication

Exact computation establishes that cubic bipartite counterexamples must have at least 60 vertices, implying a strengthened lower bound.

Cite This Study

Julius Tranquilli (2026) studied this question.

synapsesocial.com/papers/6a6d985be258b358b3c6b8e0 https://doi.org/10.5281/zenodo.21695514

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A 60-Vertex Lower Bound for Cubic Bipartite Counterexamples to the Erdős–Gyárfás Conjecture

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Discussion

Implication

Cite This Study

A 60-Vertex Lower Bound for Cubic Bipartite Counterexamples to the Erdős–Gyárfás Conjecture

Key Points

Discussion

Implication

Cite This Study

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