Corpus ID: 236493779

On the spanning structure hierarchy of 3-connected planar graphs

@inproceedings{Lo2021OnTS,
  title={On the spanning structure hierarchy of 3-connected planar graphs},
  author={On-Hei Solomon Lo},
  year={2021}
}
The prism over a graph G is the Cartesian product of G with the complete graph K2. G is prism-hamiltonian if the prism over G has a Hamilton cycle. A good even cactus is a connected graph in which every block is either an edge or an even cycle, and every vertex is contained in at most two blocks. It is known that good even cacti are prism-hamiltonian. Indeed, showing the existence of a spanning good even cactus has become one of the most common techniques in proving prism-hamiltonicity… Expand

Figures from this paper

References

SHOWING 1-10 OF 21 REFERENCES
A characterization of Hamiltonian prisms
  • P. Paulraja
  • Mathematics, Computer Science
  • J. Graph Theory
  • 1993
A characterization is established for a graph G to have a Hamilton cycle in G × K2, the prism over G. Moreover, it is shown that every 3-connected graph has a 2-connected spanning bipartite subgraph.Expand
A counterexample to prism-hamiltonicity of 3-connected planar graphs
  • S. Spacapan
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 2021
TLDR
A counterexample to the conjecture that every 3-connected planar graph is prism-hamiltonian is constructed and it is shown that this conjecture is false. Expand
Prism-hamiltonicity of triangulations
TLDR
It is proved that triangulations of the plane, projective plane, torus, and Klein bottle are prism-hamiltonian, and that every 4-connected triangulation of a surface with sufficiently large representativity is prism-Hamiltonian. Expand
The Chvátal-Erdős condition for prism-Hamiltonicity
TLDR
It is proved that α ( G) ≤ 2 κ ( G ) implies the stronger condition, prism-Hamiltonicity of G. Expand
Hamilton cycles in prisms
TLDR
Examining classical problems on hamiltonicity of graphs in the context of having a hamiltonian prism is shown to be an interesting relaxation of being Hamiltonian. Expand
On hamiltonian cycles in the prism over the odd graphs
TLDR
It is shown that the prism over Ok is hamiltonian for all k even and not just for n = 2k + 1, where n is a special case of Kneser graph. Expand
Toughness and prism-hamiltonicity of P4-free graphs
TLDR
It is shown that for the class of P_4-free graphs, the three properties of being prism-hamiltonian, having a spanning $2$-walk, and being $\frac{1}{2}$-tough are all equivalent. Expand
2-walks in 3-connected Planar Graphs
In this we prove that every 3-connected planar graph has closed walk each vertex, none more than twice, such that any vertex visited twice is in a vertex cut of size 3. This both Tutte's Theorem thatExpand
On 3-polytopes with non-Hamiltonian prisms
TLDR
It is proved that there exists an infinite family of counterexamples to the Rosenfeld-Barnette conjecture, each member of which has maximum degree 37, is of girth 4, and contains no oddlength face with length less than k for a given odd integer k. Expand
2-Walks in Circuit Graphs
Abstract We prove the conjecture of Jackson and Wormald that every 3-connected planar graph has a closed walk visiting every vertex once or twice. This strengthens Barnette′s Theorem that everyExpand
...
1
2
3
...