Abstract: In this talk I will discuss the well-known conjecture that there are no snarks amongst Cayley graphs. I will present an innovative approach in solving this conjecture combining the theory of Cayley maps and the existence of independent set of vertices whose complement induces a forest in arc-transitive graphs admitting a group of automorphisms acting regularly on the set of arcs with cyclic vertex stabilizer, together with some partial results obtained thus far.
This is a joint work with Ademir Hujdurovic and Dragan Marusic.

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20.02.2012 Lecturer: dr. Vito Vitrih

Title: Pythagorean-hodograph curves

Abstract: Polynomial Pythagorean-hodograph curves (PH curves) have been introduced in 1990 by Farouki and Sakkalis. They are characterized by the property that their parametric speed, i.e., the derivative of the arc length with respect to the curve parameter, is a polynomial function. Polynomial PH curves form an important class of parametric polynomial curves for which the arc length can be computed exactly and their offsets (parallel curves) are rational curves. This makes them very useful in many practical applications, e.g. in CAD/CAM systems, robotics, animation, NC machining, spatial path planning based on rotation-minimizing frames, etc.

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06.02.2012 Lecturer: Hiroki Koike

Title: Isomorphic Tetravalent cyclic Haar graphs

Abstract: Let S be a subset of the cyclic group Zn. The cyclic Haar graph H(Zn,S) is the bipartite graph with vertex set two copies of the cyclic group and edges {x,y} where x and y are in Zn and x-y is in S. We give necessary and sufficient conditions for the isomorphism of two connected cyclic Haar graphs of valency 4.

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