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’ and ‘all’? Remarkably, little is known, and even the problem of whether triplets of longest paths necessarily share a common vertex remains open.

How to participate in this seminar:

1. Book your nearest ACE facility;

2. Notify the seminar convenor at La Trobe University  (Yuri Nikolayevsky) to notify you will be participating.

No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)

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