Geodesic
Counting the regions in a regular drawing of kn,n
Journal of integer sequences, Tome 13 (2010) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We calculate here both exact and asymptotic formulas for the number of regions enclosed by the edges of a regular drawing of the complete bipartite graph $K_{n,n}$. This extends the work of Legendre, who considered the number of crossings arising from such a graph. We also show that the ratio of regions to crossings tends to a rational constant as $n$ increases without limit.
Classification : 05C62, 05A15, 05A16, 11A05
Keywords: complete bipartite graph, crossing, greatest common divisor, region 
@article{JIS_2010__13_8_a1,
     author = {Griffiths, Martin},
     title = {Counting the regions in a regular drawing of kn,n},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {13},
     number = {8},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_8_a1/}
}
TY  - JOUR
AU  - Griffiths, Martin
TI  - Counting the regions in a regular drawing of kn,n
JO  - Journal of integer sequences
PY  - 2010
VL  - 13
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2010__13_8_a1/
LA  - en
ID  - JIS_2010__13_8_a1
ER  - 
%0 Journal Article
%A Griffiths, Martin
%T Counting the regions in a regular drawing of kn,n
%J Journal of integer sequences
%D 2010
%V 13
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2010__13_8_a1/
%G en
%F JIS_2010__13_8_a1
Griffiths, Martin. Counting the regions in a regular drawing of kn,n. Journal of integer sequences, Tome 13 (2010) no. 8. http://geodesic.mathdoc.fr/item/JIS_2010__13_8_a1/