Year: 2024
Type: preprint
Abstract: Chess graphs encode the moves that a particular chess piece can make on an $m\times n$ chessboard. We study through these graphs through the lens of chip-firing games and graph gonality. We provide upper and lower bounds for the gonality of king's, bishop's, and knight's graphs, as well as for the toroidal versions of these graphs. We also prove that among all chess graphs, there exists an upper bound on gonality solely in terms of $\min\{m,n\}$, except for queen's, toroidal queen's, rook's, and toroidal bishop's graphs.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4392576607