# Hamiltonian cycles in annular decomposable Barnette graphs

@article{Bej2020HamiltonianCI,
title={Hamiltonian cycles in annular decomposable Barnette graphs},
author={Saptarshi Bej},
journal={Journal of Discrete Mathematical Sciences and Cryptography},
year={2020}
}
• Saptarshi Bej
• Published 15 August 2020
• Mathematics
• Journal of Discrete Mathematical Sciences and Cryptography
Barnette's conjecture is an unsolved problem in graph theory. The problem states that every 3-regular (cubic), 3-connected, planar, bipartite (Barnette) graph is Hamiltonian. Partial results have been derived with restrictions on number of vertices, several properties of face-partitions and dual graphs of Barnette graphs while some studies focus just on structural characterizations of Barnette graphs. Noting that Spider web graphs are a subclass of Annular Decomposable Barnette (ADB graphs…
• Mathematics
J. Graph Theory
• 2021
This and other results of this paper establish partial solutions of Barnette's Conjecture according to which every 3‐connected cubic planar bipartite graph is hamiltonian.
It is shown that P has at least 3 2 | P* | Δ 2 ( P ∗ ) different Hamilton cycles.
• Mathematics
• 2020
Abstract Let G = (V, E) be a graph with set of vertices V and set of edges E. An independent set in G is a subset S of V such that no two vertices of S are mutually adjacent. E. Sampathkumar et al.
• Mathematics
Discret. Math. Theor. Comput. Sci.
• 2018
The Thrackle Conjecture is proved for thrackle drawings all of whose vertices lie on the boundaries of connected domains in the complement of the drawing.
Let $$\mathcal{B}$$B denote the class of all 3-connected cubic bipartite plane graphs. A conjecture of Barnette states that every graph in $$\mathcal{B}$$B has a Hamilton cycle. A cyclic sequence of