Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A saw-toothed chessboard, or STC for short, is a kind of chessboard whose boundary forms two staircases from left down to right without any hole inside it. A rook at square (i, j) can dominate the squares in row i and in column j. The rook problem of an STC is to determine the minimum number of rooks that can dominate all squares of the STC. ,  model an STC by two particular graphs: a rook graph and a board graph.  show that for an STC, the rook graph is the line graph of the board graph, and the board graph is a bipartite permutation graph. Thus, the rook problem on STCs can be solved by any algorithm for solving the edge domination problem on bipartite permutation graphs. c 2008 Elsevier Ltd. All rights reserved.
['Hon-Chan Chen', 'Ting-Yem Ho']
I am writing a research paper on a idea The rook problem on saw-toothed chessboards
[{"from": "human", "value": "I am writing a research paper on a idea The rook problem on saw-toothed chessboards"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A saw-toothed chessboard, or STC for short, is a kind of chessboard whose boundary forms two staircases from left down to right without any hole inside it. A rook at square (i, j) can dominate the squares in row i and in column j. The rook problem of an STC is to determine the minimum number of rooks that can dominate all squares of the STC. ,  model an STC by two particular graphs: a rook graph and a board graph.  show that for an STC, the rook graph is the line graph of the board graph, and the board graph is a bipartite permutation graph. Thus, the rook problem on STCs can be solved by any algorithm for solving the edge domination problem on bipartite permutation graphs. c 2008 Elsevier Ltd. All rights reserved."}]