کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9655158 | 684032 | 2005 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Generalized knight's tours on rectangular chessboards
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In [Math. Mag. 64 (1991) 325-332], Schwenk has completely determined the set of all integers m and n for which the mÃn chessboard admits a closed knight's tour. In this paper, (i) we consider the corresponding problem with the knight's move generalized to (a,b)-knight's move (defined in the paper, Section 1). (ii) We then generalize a beautiful coloring argument of Pósa and Golomb to show that various mÃn chessboards do not admit closed generalized knight's tour (Section 3). (iii) By focusing on the (2,3)-knight's move, we show that the mÃn chessboard does not have a closed generalized knight's tour if m=1,2,3,4,6,7,8 and 12 and determine almost completely which 5kÃm chessboards have a closed generalized knight's tour (Section 4). In addition, (iv) we present a solution to the (standard) open knight's tour problem (Section 2).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 150, Issues 1â3, 1 September 2005, Pages 80-98
Journal: Discrete Applied Mathematics - Volume 150, Issues 1â3, 1 September 2005, Pages 80-98
نویسندگان
G.L. Chia, Siew-Hui Ong,