# Algebraic, Topological and Complexity Aspects of Graph Covers 2013

from January 28, 2013 to February 1, 2013 (UTC)
Bovec, Slovenia
UTC timezone
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Displaying 11 contributions out of 11
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 Mr. Rok POžAR
\documentclass{article} \usepackage{amsthm,amsfonts,amsmath,amssymb} \usepackage[cp1251]{inputenc} \usepackage[english,russian]{babel} \usepackage[final]{graphicx} \textwidth 11.5cm \textheight 16cm \begin{document} \begin{center} \textbf{\Large Branched coverings of graphs and related topics} \\ \vspace{\baselineskip} {\large Alexander Mednykh} \\ \vspace{\baselineskip} So ... More
Presented by Prof. Alexander Mednykh MEDNYKH
We construct and classify the regular maps which are cyclic coverings of the platonic maps in the general case that the branched points may occur simultaneously over the vertices and face-centres of the base maps. Each such map is given by a presentation consisting of six interdependent integer parameters satisfying a system of congruence equations. The method involves studying the lattice struc ... More
Presented by Mr. Kan HU
The list homomorphism problem generalizes several well known algorithmic problems, from the colouring and homomorphism problems to pre-colouring and surjective mapping problems. I will survey what is known for both undirected and directed graphs, with emphasis on recent results regarding the existence of polynomial or logspace algorithms.
Presented by Dr. Pavol HELL
We say that a homomorphism $f\colon G \to H$ is locally injective (locally surjective, locally bijective, quasi-covering, resp.), if for every vertex $v$ of $G$ is the mapping $f|_{N_G(v)} \colon N_G(v) \to N_H(f(v))$ injective (surjective, bijective, $c_v$-fold, resp.). For such mapping we define corresponding decision problem {\sc $H$-LIHom} ({\sc $H$-LSHom}, {\sc $H$-LBHom}, {\sc $H$-QCover}, ... More
Presented by Mr. Marek TESAR
Lists of discrete group actions have many applications in different fields of mathematics. In combinatorics they can be used to derive lists of highly symmetrical maps of fixed genus: regular maps, vertex-transitive maps, Cayley maps or edge-transitive maps. The classification of actions of cyclic groups play the crucial role for enumeration problems of combinatorial objects, i.e. maps, graphs and ... More
Presented by Mr. Ján KARABáš
Maps are embeddings of graphs in surfaces, and regular maps are the most symmetric of these. David Surowski and I (EJC 21 (2000), 333-345, 407-418) classified the regular cyclic coverings of the Platonic maps, branched over the vertices, edges or faces. I shall describe how this can be extended to elementary abelian (and ultimately all abelian) coverings, using the G-module structure of the homolo ... More
Presented by Prof. Jones GARETH A.
At last year's ATCAGC workshop (at Eugene) I presented new methods for finding symmetric regular covers of symmetric graphs, which my PhD student Jicheng Ma and I had applied to find all symmetric regular covers of $K_4$, $K_{3,3}$ and $Q_3$ with an abelian covering group. Since then we did the same for the Petersen and Heawood graphs. The case of the Heawood graph was particularly challenging, ... More
Presented by Prof. Marston CONDER
In order to complete a result by C. Praeger and A. Gardiner on 4-valent symmetric graphs we apply the lifting method for elementary-abelian covering projections. In particular, for $p \noteq 2$, the graphs whose quotient over some $p$-elementary abelian group of automorphisms is a cycle, are described in terms of linear codes. Joint work with A. Malni\v c and P. Poto\v cnik.
Presented by Dr. Bostjan KUZMAN
Let $G$ and $H$ be connected graphs. We say that $G$ covers $H$ if there exists a locally-bijective homomorphism $f$ from $G$ to $H$. For a~vertex $v \in H$, its fiber $f^{-1}(v)$ is the set of the vertices of $G$ which are mapped by $f$ to $v$. A covering $f$ is regular if the group $\textrm{Aut}(G)$ acts transitively on every fiber of $f$. Roughly speaking, the copies of $H$ in $G$ are conne ... More
Presented by Mr. Pavel KLAVIK
Each finite graph on n vertices determines a special (n-1)-fold covering graph that we call TheCover. Several equivalent denitions and some surprising facts about this remarkable construction are presented. This is a joint work with Marko Boben, Aleksander Malnič and Arjana Žitnik.
Presented by Prof. Tomaz PISANSKI