Raziskovalni matematični seminar - Arhiv
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28.03.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: dr.Martin Milanič
Title: Towards a combinatorial characterization of equistable graphs - partial results on a conjecture of Orlin
Abstract: Equistable graphs are graphs for which there exists a linear functional which characterizes the maximal stable sets of the graph. (A stable set is a set of pairwise non-adjacent vertices.) A conjecture due to Jim Orlin states that every equistable graph is a general partition graph (i.e., the intersection graph of a set system over a finite set S such that the maximal stable sets correspond precisely to the partitions of S using only sets from the family).
Orlin's conjecture holds within the class of chordal graphs; if true in general, it would provide a combinatorial characterization of equistable graphs. In this talk, we will explain the known connections between general partition graphs, equistable graphs, and triangle graphs, and show some partial results on Orlin's conjecture. In particular, we will present a complete characterization of equistable graphs decomposable with respect to the Cartesian or the tensor product.
SLIDES FROM THE LECTURE ARE AVAILABLE HERE: DOWNLOAD!
21.03.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: mag. Boštjan Frelih
Title: Classification of cubic symmetric fivecirculants
Abstract: A fivecirculant is a graph admitting an automorphism having five cycles of equal length in its cycle decomposition. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. In this talk, we give a classification of cubic symmetric fivecirculants.
14.03.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: dr. Vito Vitrih
Title: High order parametric polynomial approximation of conic sections
Abstract: In this talk a particular shape preserving parametric polynomial approximation of conic sections will be presented. An ellipse and a hyperbola can be represented in a parametric form using e.g. trigonometric and hyperbolic functions. But, in contrast to a parabola, they do not have a parametric polynomial parameterization. In many applications a parametric polynomial approximation of conic sections is needed and it is important to derive accurate polynomial approximants. We will derive polynomial approximants with the highest possible approximation order in a closed form.
Slides from the talk are available here: Download!
07.03.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: Ademir Hujdurović
Title: Bipartite locally distance transitive graphs.
Abstract: In this talk we introduce the definition of locally distance transitive graph, and prove some basic properties. We also discuss possible characterization of bipartite locally distance transitive graphs.
