# International Conference on Graph Theory and Combinatorics

16-18 May 2014
Rogla, Slovenia
UTC timezone
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## Contribution List

Displaying 16 contributions out of 16
We show that a simple expression, that employs a single square root and integer division, yields a surprisingly good estimate of the largest eigenvalue of adjacency matrix of a graph.
Presented by Prof. Dragan STEVANOVIC
It is a well established but highly nontrivial fact that planar sets are aspherical (Zastow, Cannon/Conner/Zastrow ). We discuss another relatively simple and canonical strategy to prove planar sets are aspherical, employing projections of Hadamard spaces, realized as universal covers of PL planar compacta.
Presented by Prof. Paul FABEL
The Chinese restaurant process is a way to create random premutations that are not equally likely. One can associate a random measure to the process and examine the limiting behaviour of this random measure which gives asymptotic information on the structure of cycles.
Presented by Prof. Mihael PERMAN
Combinatorial treatment of graph coverings in terms of voltages has received considerable attention over the years, with its main incentive in constructing regular coverings of graphs with specific symmetry properties. Accordingly, one would like to find algorithms that would deliver answers to certain natural questions regarding symmetry issues of graphs and their coverings; this adds further ... More
Presented by Dr. Rok POZAR
One of the big difficulties in compex analysis is construction of globally defined mappings on complex manifolds. Compact manifolds only have trivial mappings (into $\Cc^n$) and on the other side Stein manifolds have plenty. The next class with a large family of mappings are 1-convex manifolds. In particular, we are interested in constructing mappings with polynomial growth at the boundary in the ... More
Presented by Dr. Jasna PREZELJ PERMAN
Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. The set of 148 discrete Adriatic indices has ... More
Presented by Alexander VASILYEV
Since Euler's conceptualization of 7 bridges of Königsberg in 1735, Graph theory is nowadays a well established field of mathematics, especially applied. But if today one wants to apply mathematics for modeling all kinds of systems and processes, one has to go a step further and treat vertices, edges and paths in a graph more algebraically unified. A graph is also not an object per se, but commun ... More
Presented by Viljem TISNIKAR
I first met Aleksander Malni\v c in the Spring of 1972 when we were both part of the Slovenian National team at the Yugoslavian Mathematical Olympiad. In this talk I will be reminiscing about our intersecting mathematical paths, our ups and downs, and my joy for the privilege to have been around such a brilliant but yet humble mathematician.
Presented by Prof. Dragan MARUŠIČ
A decomposition of a simple graph G=(V(G),E(G)) is a pair $[G,\mathcal{D}]$ where $\mathcal{D}$ is a set of induced subgraphs of $G$, such that every edge of $G$ belongs to exactly one subgraph in $\mathcal{D}$. A \emph{coloring} of a decomposition $[G,\mathcal{D}]$ with $k$ colors is a surjective function that assigns to edges of $G$ a color from a $k$-set of colors, such that all edg ... More
Presented by Prof. Gyorgy KISS
We show that for certain integers $n$, the problem of whether or not a circulant digraph $\Gamma$ of order $n$ is also isomorphic to a Cayley digraph of some other abelian group $G$ of order $n$ reduces to the question of whether or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group). A ne ... More
Presented by Prof. Ted DOBSON
A commutating graph of an algebra is a simple graph, where vertices are all noncentral elements of the algebra, and two vertices are connected if the corresponding elements commute. We will present some problems that are studied in relation to commuting graph.
Presented by Prof. Bojan KUZMA
Perfect nonlinear functions, also known as planar mappings, share a great deal of their their properties with another combinatorial concept known as bent functions. It turns out that hese different concepts, for instance behaving differently for different prime charactestics of their prime fields, are almost identical notions, in particular this is true if the component functions of planar map ... More
Presented by Dr. Enes PASALIC
Castelnuovo-Mumford regularity is an important graph invariant in combinatorial commutative algebra. I'll give a definition of regularity in terms of simplicial homology, which will make it clear that it is a measure of complexity of a graph. I'll then relate regularity to other graph invariants.
Presented by Prof. Russ WOODROOFE
Configurations of points and lines have Levi graphs that are well understood. These graphs are bipartite, semi-regular and have girth at least six. They reflect the property that the dual of a configuration of points and lines is again a configuration of points and lines. In case of configurations of points and circles the situation is quite different. For instance, the duality does not preserve ... More
Presented by Prof. Tomaz PISANSKI
A {\it CIS} graph is a graph in which every maximal stable set and every maximal clique intersect. A {\em well-covered} graph is a graph in which all maximal stable sets are of the same size, and {\em co-well-covered} if its complement is well-covered. A {\it circulant} is a Cayley graph of a cyclic group. A graph is said to be {\it vertex-transitive} if for every two vertices $u$ and $v$, th ... More
Zonohedra (or more generally, zonotopes) are a particular class of convex polytopes characterized by the property that all their 2-dimensional faces are centrally symmetric. We introduce a generalization of the graph of zonotopes, which we call a zonograph\/. We show through examples how zonographs can be used in the construction of $(n_k)$ configurations of points and circles. Zonographs also ... More