Glenn H. Hurlbert

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math.CO2025

Erdős-Ko-Rado Theorems for Paths in Graphs

Neal Bushaw, James Danielsson, Glenn Hurlbert

A family of sets is $s$ -intersecting if every pair of its sets has at least $s$ elements in common. It is an $s$ -star if all its members have some $s$ elements in common. A family…

math.CO2025

A New Dominating Set Game on Graphs

Sean Fiscus, Glenn Hurlbert, Eric Myzelev +1

We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vert…

math.CO2025

Intersecting Families of Spanning Trees

Peter Frankl, Glenn Hurlbert, Ferdinand Ihringer +4

A family $F$ of spanning trees of the complete graph on $n$ vertices $K_{n}$ is \emph{ $t$ -intersecting} if any two members have a forest on $t$ edges in common. We prove an…

math.CO2025

A Survey of the Holroyd-Talbot Conjecture

Glenn Hurlbert

A family of sets is intersecting if every pair of its members has an element in common. Such a family of sets is called a star if some element is in every set of the family. Given…

math.CO2023

Cup Stacking in Graphs

Paul Fay, Glenn Hurlbert, Maya Tennant

Here we introduce a new game on graphs, called cup stacking, following a line of what can be considered as $0$ -, $1$ -, or $2$ -person games such as chip firing, percolation, graph b…

math.CO2023

Thresholds for zero-sums with small cross numbers in abelian groups

Neal Bushaw, Glenn Hurlbert

For an additive group $Γ$ the sequence $S = (g_{1}, \dots, g_{t})$ of elements of $Γ$ is a zero-sum sequence if $g_{1} + \dots + g_{t} = 0_{Γ}$ . The cross number of $S$ is defined to be th…