A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give a basic theory of k-orbit maps and classify them up to k 4. “Hurwitz-like” upper...
A partial linear space is a non-empty set of points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every lin...
A map is a connected topological graph cellularly embedded in a surface. For a given graph , its genus distribution of rooted maps and embeddings on orientable and non-orientable s...
A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured in such a way that “neighbouring” hypervertices have different colours. It is bipartiteuniform i...
Abstract. A graph is connected-homogeneous if any isomorphism between finite connected induced subgraphs extends to an automorphism of the graph. In this paper we classify the cou...