Mathematical Research Seminar - Archive

In this partly historical talk I explain what is meant by combinatorics, and outline its development from ancient problems in China and India involving permutations and combinations to more recent problems in graph theory and the study of Latin squares. Many of the problems have recreational origins, such as dice games, the knight's tour problems, magic squares, and sudoku.

Everyone is welcome and encouraged to attend!

We show that if the edges or vertices of an undirected graph G can be covered by k shortest paths, then the pathwidth of G is upper-bounded by a function of k. As a corollary, we prove that the problem Isometric Path Cover with Terminals (which, given a graph G and a set of k pairs of vertices called terminals, asks whether G can be covered by k shortest paths, each joining a pair of terminals) is FPT with respect to the number of terminals. The same holds for the similar problem Strong Geodetic Set with Terminals (which, given a graph G and a set of k terminals, asks whether there exist (k choose 2) shortest paths, each joining a distinct pair of terminals such that these paths cover G). Moreover, this implies that the related problems Isometric Path Cover and Strong Geodetic Set (defined similarly but where the set of terminals is not part of the input) are in XP with respect to parameter k.

Everyone is welcome and encouraged to attend!

We're thrilled to extend an invitation to you for a workshop that's bound to be an eye-opener.

Hosted by the Andrej Marušič Institute and the Faculty of Mathematics, Natural Sciences, and Information Technologies at the University of Primorska, this event is all set to ignite your passion for algebraic combinatorics.

Our lineup of speakers, hailing from diverse backgrounds, promises to lead you on a journey through the vibrant realm of algebraic combinatorics. Whether you're a seasoned researcher or someone who simply finds the subject intriguing, this workshop guarantees to leave you both inspired and enlightened.

Save the date: Thursday, October 12. It's a day packed with groundbreaking insights, engaging discussions, and the chance to network with like-minded peers who share your fervor.