The gonality of chess graphs
arxiv(2024)
摘要
Chess graphs encode the moves that a particular chess piece can make on an
m× 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.
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