News & Events
Speaker: Guantao Chen, Regents’ Professor, Department of Mathematics and Statistics, Georgia State University
Date: May. 25, 2022
Location: Tencent Meeting
Sponsor: School of Mathematics, Shandong University
The work on finding a hamiltonian cycle in 4-connected graphs can be traced back to the early proof attempts of the four color theorem. In 1880, Tait observed that every hamiltonian plane graph is four face colorable. In this failed attempt, Tait made a couple of assumptions; one of them is that every 3-connected cubic planar graph is hamiltonian. The first counterexample was published by Tutte in 1946. On the other hand, Whitney in 1931 proved that every4-connected plane triangulation contains a Hamiltonian cycle. Whitney's theorem has been generalized to all 4-connected planar graphs by Tutte: every 4-connected planar graph contains a hamiltonian cycle.
Tutte's result has played a central role in developing topologic graph theory and has been generalized to projective-planar graphs, Klein bottles, toroidal graphs, and graphs embedded on other surfaces. Starting with a conjecture of Moon and Morser on the circumference of a planar graph, we will address the following four topics related to the Tutte Theorem.
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