Geodesic
Thinnest Packing of Cubes with a Given Number of Neighbours
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 501-507

Voir la notice de l'article provenant de la source Cambridge University Press

As a contribution to various investigations [1-11] about packing of convex bodies with certain conditions imposed on the number of neighbours of each body, V. Chvátal [12] recently proved the following theorem: If in a packing of translates of a square each square has at least six neighbours then the density of the packing is at least 11/15. 
Tóth, L. Fejes; Sauer, N. Thinnest Packing of Cubes with a Given Number of Neighbours. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 501-507. doi: 10.4153/CMB-1977-075-0
@article{10_4153_CMB_1977_075_0,
     author = {T\'oth, L. Fejes and Sauer, N.},
     title = {Thinnest {Packing} of {Cubes} with a {Given} {Number} of {Neighbours}},
     journal = {Canadian mathematical bulletin},
     pages = {501--507},
     year = {1977},
     volume = {20},
     number = {4},
     doi = {10.4153/CMB-1977-075-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-075-0/}
}
TY  - JOUR
AU  - Tóth, L. Fejes
AU  - Sauer, N.
TI  - Thinnest Packing of Cubes with a Given Number of Neighbours
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 501
EP  - 507
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-075-0/
DO  - 10.4153/CMB-1977-075-0
ID  - 10_4153_CMB_1977_075_0
ER  - 
%0 Journal Article
%A Tóth, L. Fejes
%A Sauer, N.
%T Thinnest Packing of Cubes with a Given Number of Neighbours
%J Canadian mathematical bulletin
%D 1977
%P 501-507
%V 20
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-075-0/
%R 10.4153/CMB-1977-075-0
%F 10_4153_CMB_1977_075_0

[1] 1. Tóth, Fejes L., Scheibenpackungen konstanter Nachbarnzahl, Acta Math. Acad. Sci. Hungar. 20(1969)375-381. Google Scholar

[2] 2. Robinson, R.M., Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179(1969)296-318. Google Scholar

[3] 3. Tóth, Fejes L., Remarks on a theorem of R. M. Robinson, Studia Sci. Math. Hungar. 4 (1969)441-445. Google Scholar

[4] 4. Wegner, G., Bewegungsstabile Packungen konstanter Nachbarnzahl, Studia Sci. Math. Hungar. 6(1971)431-438. Google Scholar

[5] 5. Tóth, Fejes G., ?ber Parkettierungen konstanter Nachbarnzahl, Studia Sci. Math. Hungar. 6 (1971)133-135. Google Scholar

[6] 6. Böröczky, K., Über die Newtonsche Zahl regulärer Vielecke, Periodica Math. Hungar. 1 (1971) 113-119. Google Scholar

[7] 7. Linhart, J., Über einige Vermutungen von L. Fejes Tóth, Acta Math. Acad. Sci. Hungar. 24 (1973) 199-201. Google Scholar

[8] 8. Linhart, J., Endliche n-nachbam Packungen in der Ebene und auf der Kugel, Periodica Math. Hungar. 5 (1974) 301-306. Google Scholar

[9] 9. Gács, P., Packing convex sets in the plane with a great number of neighbours, Acta Math. Acad. Sci. Hungar. 23 (1972) 383-388. Google Scholar

[10] 10. Tóth, Fejes L., Five-neighbour packing of convex discs, Periodica Math. Hungar. 4 (1973) 383-388. Google Scholar

[11] 11. Makai, E. Jr., Five-neighbour packing of convex discs, Periodica Math. Hungar. 5 (1974). Google Scholar

[12] 12. Chvátal, V., On a conjoncture of Fejes Tóth, Periodica Math. Hungar, 6 (1975) 357-362. Google Scholar

Cité par Sources :