Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://www.revistas.ucr.ac.cr/index.php/matematica/oai
On the Distribution of non-attacking Bishops on a Chessboard C
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Keywords

bishop polynomials
bipartite graphs
matching
chessboard
polinomios de alfiles
grafos bipartitos
apareamiento
tablero de ajedrez

How to Cite

Ansari Wahid, S. (2001). On the Distribution of non-attacking Bishops on a Chessboard C. Revista De Matemática: Teoría Y Aplicaciones, 8(1), 47–62. https://doi.org/10.15517/rmta.v8i1.197

Abstract

It is shown how the placement of non-attacking bishops on a chessboard C is related to the matching polynomial of a bipartite graph. Reduction algorithms for finding the bishop polynomial of C are given. We interpret combinatorially the coefficients of this polynomial and construct some interesting boards. Some applications of the bishop polynomials are given.

https://doi.org/10.15517/rmta.v8i1.197
PDF (Español (España))

References

Farrell, E.J.; Whitehead, E.G. Jr.(1992) “Connections between the matching and chromatic polynomials”, Internat. J. Math and Math. Sci. 15(4): 757–766.

Read, R.C. (1968) “An introduction to chromatic polynomials”, J. Combin. Theory 4: 52–71.

Riordan, J. (1980) An Introduction to Combinatorial Analysis. Princeton University Press, Princeton, New Jersey.

Sloane, N.J.A.; Plouffe, S. (1995) The Encyclopedia of Integer Sequences. Academic Press, London and New York.

Wahid, S.A. (1990) A Matrix Approach to Matching Polynomials. Ph.D. Thesis, University of the West Indies, St. Augustine, Trinidad, W.I.

Wahid, S.A. (1983) On the Matching Polynomials of Graphs. M. Phil. Thesis, University of the West Indies, St. Augustine, Trinidad, W.I.

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