Steinhaus棋盘问题是波兰著名数学家Steinhaus在其著作Problem and Discussion中提出的一个比较有趣的问题,文献[2-3]分别用不同的方法给以证明,但是证明过程较为复杂.通过比较直观的方式给出了该问题的简单证明,并给出了该问题在图论...Steinhaus棋盘问题是波兰著名数学家Steinhaus在其著作Problem and Discussion中提出的一个比较有趣的问题,文献[2-3]分别用不同的方法给以证明,但是证明过程较为复杂.通过比较直观的方式给出了该问题的简单证明,并给出了该问题在图论中的等价命题.展开更多
Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem...Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.展开更多
文摘Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.
