The Mathematics of Chessboard Problems. Simple exact formulas are given for the expected value of the number of perfect matchings in random polyomino chain graphs and for the asymptotic behavior of this expectation. Practice online or make a printable study sheet. A random polyomino chain is a subgraph of a polyomino graph. Three questions are posed:
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The queen domination problem
Domination of the rectangular queen's graph. Velucchi also considers the nondominating queens problem, which consists of placing queens on an order chessboard to leave a maximum number of unattacked vacant cells. Considerable research in statistical physics and structural chemistry has been devoted to polyomino graphs   . Contact the MathWorld Team. Based on this result, we have that the maximum forcing number of a polyomino graph can be computed in polynomial time. Fri Jan 18 The number of solutions for queens with odd are 1, 0, 10, 28, 0, 88,