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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
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Presented by Mr. Rok POžAR

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\textbf{\Large Branched coverings of graphs and related topics}
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{\large Alexander Mednykh}
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So
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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
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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},
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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
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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
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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,
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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
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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