3 papers
math.CO2025
Chromatic numbers with open and nonzero local modular constraints
Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski +9
In this paper, we explore chromatic numbers subject to various local modular constraints. For fixed , we consider proper integer colorings of a graph for which the closed an…
math.CO2025
Chromatic numbers with closed local modular constraints
Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski +9
Generalizing the notion of odd-sum colorings, a -labeling of a graph is called a closed coloring with remainder if the closed neighborhood label sum of ea…
math.CO2022
On the -hull number and infecting times of generalized Petersen graphs
Daniel Herden, Jonathan Meddaugh, Mark Sepanski +8
The -hull number of a graph is the minimum cardinality of an infecting set of vertices that will eventually infect the entire graph under the rule that uninfected nodes become…