Robert D. Luther

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math.CO2024

Existential Closure in Uniform Hypergraphs

Andrea C. Burgess, Robert D. Luther, David A. Pike

For a positive integer $n$ , a graph with at least $n$ vertices is $n$ -existentially closed or simply $n$ -e.c. if for any set of vertices $S$ of size $n$ and any set $T \subseteq S$ ,…

math.CO2022

Existential Closure in Line Graphs

Andrea C. Burgess, Robert D. Luther, David A. Pike

A graph $G$ is {\it $n$ -existentially closed} if, for all disjoint sets of vertices $A$ and $B$ with $∣ A \cup B ∣ = n$ , there is a vertex $z$ not in $A \cup B$ adjacent to each vertex o…

math.CO2022

The Edge-Connectivity of Vertex-Transitive Hypergraphs

Andrea C. Burgess, Robert D. Luther, David A. Pike

A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-…