Every pair of longest paths in a connected graph must share a common vertex. Is it also true that all of the longest paths in a connected graph must share a common vertex? The answer is no, not in general, although there are classes of graphs for which it is true. What happens between ‘two’ […]
The shape of a geometric object determines its resonant frequencies, or spectrum. I will talk about some new and old results describing the kinds of shapes that optimise various spectral quantities. How to participate in this seminar: 1. Book your nearest ACE facility; 2. Notify the seminar convenor at La Trobe University (Yuri Nikolayevsky) to […]
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