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7 papers · 1 filter
Rainbow numbers of for
Kean Fallon, Colin Giles, Hunter Rehm +2
Consider the set and an equation . The rainbow number of for , denoted , is the smallest number of colors such that…
Properties of a -analogue of zero forcing
Steve Butler, Craig Erickson, Shaun Fallat +6
Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation…
Anti-van der Waerden numbers on Graphs
Zhanar Berikkyzy, Alex Schulte, Elizabeth Sprangel +3
In this paper arithmetic progressions on the integers and the integers modulo n are extended to graphs. This allows for the definition of the anti-van der Waerden number of a graph…
Group Actions on Winning Games of Super Tic-Tac-Toe
Whitney George, Janine E. Janoski
Consider a tic-tac-toe board. In each field of the board, draw a smaller tic-tac-toe board. Now let super tic-tac-toe (STTT) be a game where each player's…
Tail diameter upper bounds for polytopes and polyhedra
J. Mackenzie Gallagher, Edward D. Kim
In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the diameters of convex polyhedra. Todd and Sukegawa-Kitahara proved tail-quasipolynomial bounds on the diameter…
Superlinear subset partition graphs with dimension reduction, strong adjacency, and endpoint count
Tristram C. Bogart, Edward D. Kim
We construct a sequence of subset partition graphs satisfying the dimension reduction, adjacency, strong adjacency, and endpoint count properties whose diameter has a superlinear a…