# 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} }

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…

## 24 References

### Hamiltonian cycles in planar cubic graphs with facial 2‐factors, and a new partial solution of Barnette's Conjecture

- MathematicsJ. 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.

### Remarks on Barnette’s conjecture

- MathematicsJ. Comb. Optim.
- 2020

It is shown that P has at least 3 2 | P* | Δ 2 ( P ∗ ) different Hamilton cycles.

### Spider web networks: a family of optimal, fault tolerant, hamiltonian bipartite graphs

- MathematicsAppl. Math. Comput.
- 2005

### The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices

- MathematicsJ. Comb. Theory, Ser. B
- 1988

### Generalization of bipartite graphs

- 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.…

### Annular and pants thrackles

- MathematicsDiscret. 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.

### On Barnette’s conjecture and the $$H^{+-}$$H+- property

- MathematicsJ. Comb. Optim.
- 2016

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…