4 papers
Impartial geodetic removing games on graphs
Bret J. Benesh, Dana C. Ernst, Marie Meyer +2
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertic…
Isomorphism Theorems for Impartial Combinatorial Games
Mikhail Baltushkin, Dana C. Ernst, Nándor Sieben
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved…
Impartial removing games on grid graphs
Bret J. Benesh, Dana C. Ernst, Marie Meyer +2
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertic…
Categories of impartial rulegraphs and gamegraphs
Bojan BaÅ¡iÄ, Paul Ellis, Dana C. Ernst +2
The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propos…