Hamiltonicity and structure of connected biclaw-free graphs

Alexey Pokrovskiy

doi:10.1016/j.dam.2026.07.015

August 14, 2026Discrete Applied MathematicsOpen Access

Hamiltonicity and structure of connected biclaw-free graphs

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Key Points

Determine whether sufficiently connected, balanced bipartite biclaw-free graphs with high minimum degree necessarily contain Hamiltonian cycles.
Structural graph-theoretic proof evaluating cycle existence in connected biclaw-free networks.
Asymptotic analysis establishing conditions on minimum degree threshold d for balanced bipartite graph partitions.
Every balanced bipartite, connected biclaw-free graph with minimum degree at or above a sufficiently large threshold d is Hamiltonian.
The result affirmatively settles the conjecture previously posed by Flandrin, Fouquet, and Li.

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Implication

Theoretical analysis proves Hamiltonicity in large balanced connected biclaw-free graphs, confirming a conjecture by Flandrin, Fouquet, and Li.

Abstract

We show that for sufficiently large d, every balanced bipartite, connected biclaw-free graph with minimum degree ≥ d is Hamiltonian. This confirms a conjecture of Flandrin, Fouquet, and Li.

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Alexey Pokrovskiy (2026) studied this question.

synapsesocial.com/papers/6a8178fcf2fb91fc834ac2ac https://doi.org/10.1016/j.dam.2026.07.015

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Hamiltonicity and structure of connected biclaw-free graphs

Key Points

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Implication

Abstract

Discussion

Cite This Study

Hamiltonicity and structure of connected biclaw-free graphs

Key Points

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Implication

Abstract

Discussion

Cite This Study

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