Name
Abstract | ||
|---|---|---|
A graph G is perihamiltonian if G itself is non-hamiltonian, yet every edge-contracted sub graph of G is hamiltonian. These graphs form a superclass of the hypohamiltonian graphs. By applying a recent result of Wiener on path-critical graphs, we prove the existence of infinitely many perihamiltonian graphs of connectivity k for any k >= 2. We also show that every planar perihamiltonian graph of connectivity k contains a vertex of degree k . This strengthens a theorem of Thomassen, and entails that if in a polyhedral graph of minimum degree at least 4 the set of vertices whose removal yields a non-hamiltonian graph is independent, the graph itself must be hamiltonian. Finally, while we here prove that there are infinitely many polyhedral perihamiltonian graphs containing no adjacent cubic vertices, whether an analogous result holds for the hypohamiltonian case remains open. (c) 2020 Elsevier Inc. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.amc.2020.125714 | APPLIED MATHEMATICS AND COMPUTATION |
Keywords | DocType | Volume |
Non-hamiltonian, Perihamiltonian, Hypohamiltonian | Journal | 392 |
ISSN | Citations | PageRank |
0096-3003 | 0 | 0.34 |
References | Authors | |
0 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Igor Fabrici | 1 | 101 | 14.64 |
| Tomáš Madaras | 2 | 112 | 11.15 |
| Maria Timkova | 3 | 0 | 0.34 |
| Nico Van Cleemput | 4 | 16 | 6.31 |
| Carol T. Zamfirescu | 5 | 38 | 15.25 |