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math.CO2025
The domatic number game played on graphs
Bert L. Hartnell, Douglas F. Rall
The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic n…
math.CO2020
On graphs having one size of maximal open packings
Bert L. Hartnell, Douglas F. Rall
A set of vertices in a graph is an open packing if no two distinct vertices in have a common neighbor. Among all maximal open packings in , the smallest cardinality…
math.CO2017
On well-covered Cartesian products
Bert L. Hartnell, Douglas F. Rall, Kirsti Wash
In 1970, Plummer defined a well-covered graph to be a graph in which all maximal independent sets are in fact maximum. Later Hartnell and Rall showed that if the Cartesian prod…