Knight’s Tours on 3 x <i>n</i>Chessboards with a Single Square Removed

• 作者: Amanda M. Miller David L. Farnsworth
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Knight’s TOUR HAMILTONIAN Cycle Forced Edge EXTENDER Board
• 年，卷（期）: 2013,（1）
• 页码范围: 56-59
• 页数: 4页
• 分类号: O1

摘要

The following theorem is proved: A knight’s tour exists on all 3 x n chessboards with one square removed unless: n is even, the removed square is (i, j) with i + j odd, n = 3 when any square other than the center square is removed, n = 5, n = 7 when any square other than square (2, 2) or (2, 6) is removed, n = 9 when square (1, 3), (3, 3), (1, 7), (3, 7), (2, 4), (2, 6), (2, 2), or (2, 8) is removed, or when square (1, 3), (2, 4), (3, 3), (1, n – 2), (2, n – 3), or (3, n – 2) is removed.