11 papers
PArcK trees can get as hot as you want
Svenja Huntemann, Neil A. McKay, Craig Tennenhouse
We consider the combinatorial game Partizan Arc Kayles as a generalization of Domineering. An extensive technical search using genetic algorithms found hot positions of temperature…
It's Hard to PArcK
Kyle Burke, Jeffrey Leman, Craig Tennenhouse
We show that Partizan Arc Kayles (PArcK), a generalization of Domineering to graphs, is PSPACE-complete via a reduction from Positive CNF and with recently-discovered techniques fo…
Col is PSPACE-complete on Triangular Grids
Kyle Burke, Craig Tennenhouse
We demonstrate that Col is PSPACE-complete on triangular grid graphs via a reduction from Bounded Two-Player Constraint Logic. This is the most structured graph family that Col is…
Forced Capture Hnefatafl
Kyle Burke, Craig Tennenhouse
We define a new, partizan, loopy combinatorial game, Forced-Capture Hnefatafl, similar to Hnefatafl, except that players are forced to make capturing moves when available. We show…
Vexing Vexillological Logic
Kyle Burke, Craig Tennenhouse
We define a new impartial combinatorial game, Flag Coloring, based on flood filling. We then generalize to a graph game, and find values for many positions on two colors. We demons…
Æquitas: Two-Player Counterfeit Coin Games
Kyle Burke, Tanya Khovanova, Joshua Lee +3
We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns w…
An investigation into the application of genetic programming to combinatorial game theory
Melissa A. Huggan, Craig Tennenhouse
Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and sol…
Metric dimension of combinatorial game graphs
Craig Tennenhouse
The study of combinatorial games is intimately tied to the study of graphs, as any game can be realized as a directed graph in which players take turns traversing the edges until r…
Packing and covering directed triangles
Jessica McDonald, Gregory J. Puleo, Craig Tennenhouse
We prove that if a directed multigraph has at most pairwise arc-disjoint directed triangles, then there exists a set of less than arcs in which meets all directed…
The Game of Blocking Pebbles
Michael Fisher, Craig Tennenhouse
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to exa…
Games from Basic Data Structures
Mara Bovee, Kyle Burke, Craig Tennenhouse
In this paper, we consider combinatorial game rulesets based on data structures normally covered in an undergraduate Computer Science Data Structures course: arrays, stacks, queues…