On Hamilton cycles in highly symmetric graphs

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• Torsten Mutze (University of Warwick)
• Thursday 26 March 2020, 15:00-16:00
• Watson LTC.

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The question whether a graph has a Hamilton cycle or not is one of the oldest and most fundamental graph-theoretic problems, and one of the prototypical NP-complete problems. In this talk I will survey some recent results on Hamilton cycles in different families of highly symmetric graphs. The starting point is our proof of the middle levels conjecture, and various other long-standing problems that we settled subsequently, including the Hamiltonicity of bipartite Kneser graphs, of sparse Kneser graphs, and cycles through any range of consecutive levels of the hypercube. I will highlight how these constructions and problems link several well-known concepts in combinatorics.

This talk is part of the Combinatorics and Probability seminar series.

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