Name
Abstract | ||
|---|---|---|
We give an overview of the most important techniques and results concerning the hamiltonian properties of planar 3-connected graphs with few 3-vertex-cuts. In this context, we also discuss planar triangulations and their decomposition trees. We observe an astonishing similarity between the hamiltonian behavior of planar triangulations and planar 3-connected graphs. In addition to surveying, (i) we give a unified approach to constructing non-traceable, non-hamiltonian, and non-hamiltonian-connected triangulations, and show that planar 3-connected graphs (ii) with at most one 3-vertex-cut are hamiltonian-connected, and (iii) with at most two 3-vertex-cuts are 1-hamiltonian, filling two gaps in the literature. Finally, we discuss open problems and conjectures. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.disc.2018.06.015 | Discrete Mathematics |
Keywords | Field | DocType |
Planar,3-connected,Polyhedron,Triangulation,Decomposition tree,Hamiltonian,Traceable,Hamiltonian-connected | Graph,Discrete mathematics,Combinatorics,Hamiltonian (quantum mechanics),Vertex (geometry),Polyhedron,Decomposition tree,Triangulation (social science),Planar,Mathematics | Journal |
Volume | Issue | ISSN |
341 | 9 | 0012-365X |
Citations | PageRank | References |
2 | 0.38 | 25 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kenta Ozeki | 1 | 138 | 36.31 |
| Nico Van Cleemput | 2 | 16 | 6.31 |
| Carol T. Zamfirescu | 3 | 38 | 15.25 |