Univerza na Primorskem Fakulteta za matematiko, naravoslovje in informacijske tehnologije
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# Raziskovalni matematični seminar - Arhiv

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Datum in ura / Date and time: 27.1.20
(10:00 -- 11:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Meike Hatzel (TU Berlin, Germany)
Naslov / Title: Avoidable paths in graphs
Vsebina / Abstract:

We prove a recent conjecture of Beisegel et al.~that for every positive integer $k$, every graph containing an induced $P_k$ also contains an avoidable $P_k$. Avoidability generalises the notion of simpliciality best known in the context of chordal graphs. The conjecture was only established for $k \in \{1,2\}$ (Ohtsuki et al.~1976, and Beisegel et al.~2019, respectively). Our result also implies a result of Chv\'atal et al.~2002, which assumed cycle restrictions. We provide a constructive and elementary proof, relying on a single trick regarding the induction hypothesis.
This is joint work with  Marthe Bonamy, Oscar Defrain and Jocelyn Thiebaut.

Datum in ura / Date and time: 13.1.20
(10:00 -- 11:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Gyula Y. Katona (Budapest University of Technology and Economics, Hungary)
Naslov / Title: Minimally t-Tough Graphs
Vsebina / Abstract:

A graph G is minimally t-tough if the toughness of G is t and the deletion of any edge from G decreases the toughness. Kriesell conjectured that for every minimally1-tough graph the minimum degree δ(G) = 2. It is natural to generalize this for other t values: Every minimally t-tough graph has a vertex of degree ceil(2t). In the present talk we investigate different questions related to this conjecture. The conjecture seems to be hard to prove, so we tried to prove it for some special graph classes. It turned out, that in some cases the conjecture is true because there are very few graphs that satisfy the conditions. On the other hand, we have evidence using complexity theory, that this is not the situation for some other graph classes. Many open questions remain.

This is joint work with Kitti Varga, István Kovács, Dániel Soltész.

Datum in ura / Date and time: 6.1.20
(10:00 -- 11:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Nino Bašić (UP FAMNIT)
Naslov / Title: Point-ellipse and some other exotic configurations
Vsebina / Abstract:

In this talk, we introduce point-ellipse configurations and point-conic configurations. We present some of their basic properties and describe two interesting families of balanced point-conic 6-configurations. The construction of the first family is based on Carnot's theorem, whilst the construction of the second family is based on the Cartesian product of two regular polygons. Finally, we investigate a point-ellipse configuration based on the regular 24-cell.

This is joint work with Gábor Gévay, Jurij Kovič and Tomaž Pisanski.