Covering a rectangle with six and seven circles

Discrete Applied Mathematics

Volumn 99, Issue 1-3, 2000, Pages 149-156

  Melissen, J B M ^a   Schuur, P C ^b  

^a Univ Higher Educ 'S hertogenbosch   (Netherlands)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Primary 52C15

Indexed keywords

EID: 0002152445     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00130-4     Document Type: Article

References (10)

1. E.H.L. Aarts, J.H.M. Korst, Simulated Annealing and Boltzmann Machines, Wiley, Chichester, 1989.
2. H.T. Croft, K.J. Falconer, R.K. Guy, Unsolved Problems in Geometry, Springer, Berlin, 1991.
3. Heppes A., Melissen J.B.M. Covering a rectangle with equal circles. Period. Math. Hungar. 34:1997;63-79.
4. Kirkpatrick S., Gelatt C.D. Jr., Vecchi M.P. Optimization by simulated annealing. Science. 220:1983;671-680.
5. J.B.M. Melissen, Packing and Covering with Circles, Ph.D. Thesis, University of Utrecht, 1997.
6. Melissen J.B.M., Schuur P.C. Improved coverings of a square with six and eight equal circles. Electron. J. Combin. 3:1996;R32.
7. J.B.M. Melissen, P.C. Schuur, A. Heppes, Zs. Gáspár, T. Tarnai, New circle coverings of an equilateral triangle, accepted for publication.
8. J. Pach, P.K. Agarwal, Combinatorial Geometry, Wiley, New York, 1995.
9. Tarnai T., Gáspár Zs. Covering a square by equal circles. Elem. Math. 50:1995;167-170.
10. Verblunsky S. On the least number of unit circles which can cover a square. J. London Math. Soc. 24:1949;164-170.