Hamiltonicity and structure of connected biclaw-free graphs

TL;DR

This paper proves that large enough balanced bipartite, connected biclaw-free graphs with high minimum degree are Hamiltonian, confirming a conjecture in graph theory.

Contribution

It establishes a Hamiltonicity result for a class of bipartite graphs, confirming a conjecture and extending understanding of graph structure.

Findings

Large balanced bipartite biclaw-free graphs with high minimum degree are Hamiltonian.

Confirms a conjecture by Flandrin, Fouquet, and Li.

Provides conditions under which such graphs are guaranteed to contain Hamilton cycles.

Abstract

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