The Maximum Queens Problem with Pawns

Chatham, Doug

doi:10.1515/rmm-2016-0010

Cited by 1 publication

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since chess queens do not move through other pieces, placing pawns on a board may increase the maximum number of independent queens we can put on that board. In [3] it is noted that the maximum number of mutually nonattacking queens that can be placed on an n × n board with pawns is if n is odd. The argument divides the board into 2 × 2 blocks and notes that each block can take at most one queen, regardless of how many pawns are on the board.…”

Section: What Can Be Said About the Domination Parameters Of Other Shmentioning

confidence: 99%

See 1 more Smart Citation

Independence and domination on shogiboard graphs

Chatham

2017

Recreational Mathematics Magazine

Self Cite

View full text Add to dashboard Cite

Given a (symmetrically-moving) piece from a chesslike game, such as shogi, and an n × n board, we can form a graph with a vertex for each square and an edge between two vertices if the piece can move from one vertex to the other. We consider two pieces from shogi: the dragon king, which moves like a rook and king from chess, and the dragon horse, which moves like a bishop and rook from chess. We show that the independence number for the dragon kings graph equals the independence number for the queens graph. We show that the (independent) domination number of the dragon kings graph is n − 2 for 4 n 6 and n − 3 for n 7. For the dragon horses graph, we show that the independence number is 2n − 3 for n 5, the domination number is at most n − 1 for n 4, and the independent domination number is at most n for n 5.

show abstract

Section: What Can Be Said About the Domination Parameters Of Other Shmentioning

confidence: 99%

“…That argument also works for dragon kings and dragon horses. So, as [3] asks for queens, how many pawns are needed to allow the maximum number of dragon kings or dragon horses on the board?…”

Section: What Can Be Said About the Domination Parameters Of Other Shmentioning

confidence: 99%

Independence and domination on shogiboard graphs

Chatham

2017

Recreational Mathematics Magazine

Self Cite

View full text Add to dashboard Cite

show abstract

The Maximum Queens Problem with Pawns

Cited by 1 publication

References 2 publications

Independence and domination on shogiboard graphs

Independence and domination on shogiboard graphs

Contact Info

Product

Resources

About