Tutte's Hamilton Cycle Theorem and Beyond

Xingxing Yu
1 Center for Combinatorics, LPMC, Nankai University, Tianjin 300071,
P. R. China
2 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA


Abstract

Tutte proved that every finite, $4$-connected, planar graph contains a
Hamilton cycle. I will discuss variations and extensions of this theorem by relaxing Tutte's conditions. This will lead to topics about infinite graphs, surfaces, graph minors, and approximation algorithms. I will also mention an application of Tutte's theorem to a problem in geometric knot theory.