Abstractions and Analyses of Grid Games

In this paper, we define various combinatorial games derived from the NQueens Puzzle and scrutinize them, particularly the Knights Game, using combinatorial game theory and graph theory. The major result of the paper is an original method for determining who wins the Knights Game merely from the board\u27s dimensions. We also inspect the Knights Game\u27s structural similarities to the Knight\u27s Tour and the Bishops Game, and provide some historical background and real-world applications of the material

Coloring square-free Berge graphs

We consider the class of Berge graphs that do not contain an induced cycle of length four. We present a purely graph-theoretical algorithm that produces an optimal coloring in polynomial time for every graph in that class

Coloring Square-free Berge Graphs

We consider the class of Berge graphs that do not contain a chordless cycle of length $4$. We present a purely graph-theoretical algorithm that produces an optimal coloring in polynomial time for every graph in that class