arXiv subjects

Primoz Potocnik

Publications and source records attributed to Primoz Potocnik.

21 records · Page 2Linked to original sources

arXiv2010

Tetravalent arc-transitive graphs with unbounded vertex-stabilisers

It has long been known that there exist finite connected tetravalent arc-transitive graphs with arbitrarily large vertex-stabilisers. However, beside a well known family of exceptional graphs, related to the lexicographic product of a cycle with an edgeless graph on two vertices, only a few such infinite families of graphs are known. In this paper, we present two more families of tetravalent arc-transitive graphs with large vertex-stabilisers, each significant for its own reason.

math.CO↗

arXiv2008

A note on 2-subset-regular self-complementary 3-uniform hypergraphs

We show that a 2-subset-regular self-complementary 3-uniform hypergraph with $n$ vertices exists if and only if $n\ge 6$ and $n$ is congruent to 2 modulo 4.

math.CO↗

arXiv2008

Counting One-Vertex Maps

The number of distinct maps (pre-maps) with a single vertex and valence $d$ is computed for any value of $d$. The types of maps (pre-maps) that we consider depend on whether the underlaying graph (pre-graph) is signed or unsigned and directed or undirected.

math.CO↗