| Presentation | 2012-12-10 Hamiltonicity of 4-connected projective-planar graphs Ken-ichi Kawarabayashi, Kenta Ozeki, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Abstract A graph G is called hamiltonian-connected if for any two vertices u and v, there is a hamiltonian path between u and v. In this talk, we prove the following; Every 4-connected projective planar graph is hamiltonian-connected. This proves a conjecture of Dean [1] in 1990. Moreover, this generalizes the following two results; (1) Thomassen's result [3] in 1983, which states that every 4-connected planar graph is hamiltonian-connected (which generalizes the old result of Tutte [4] in 1956, which states that every 4-connected planar graph is hamiltonian). (2) Thomas and Yu's result [2] in 1994, which says that every 4-connected projective planar graph is hamiltonian. Our result is best possible in many senses. First, we cannot lower the connectivity 4. Secondly, we cannot generalize our result to a surface with higher genus (i.e, there is a 4-connected graph on the torus which is not hamiltonian-connected). Our proof is constructive in the sense that there is a polynomial time (in fact, 0(n^2) time) algorithm to find, given two vertices in a 4-connected projective planar graph, a hamiltonian path between these two vertices. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Hamiltonian / Hamiltonian-connected / projective plane / 4-connected |
| Paper # | COMP2012-46 |
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| Committee | COMP |
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| Conference Date | 2012/12/3(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Theoretical Foundations of Computing (COMP) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Hamiltonicity of 4-connected projective-planar graphs |
| Sub Title (in English) | |
| Keyword(1) | Hamiltonian |
| Keyword(2) | Hamiltonian-connected |
| Keyword(3) | projective plane |
| Keyword(4) | 4-connected |
| 1st Author's Name | Ken-ichi Kawarabayashi |
| 1st Author's Affiliation | National Institute of Informatics() |
| 2nd Author's Name | Kenta Ozeki |
| 2nd Author's Affiliation | National Institute of Informatics |
| Date | 2012-12-10 |
| Paper # | COMP2012-46 |
| Volume (vol) | vol.112 |
| Number (no) | 340 |
| Page | pp.pp.- |
| #Pages | 22 |
| Date of Issue | |