Geodesic
On the maximum number of non-intersecting diagonals in an array
Journal of integer sequences, Tome 20 (2017) no. 2
We investigate the total number of diagonals that can be placed in the unit squares of a given grid in such a way that no two diagonals have a common point. We develop theoretical and computational results for square and rectangular shaped grids, and extend the problem to three-dimensional arrays. We pose some open questions for further investigation.
Classification : 05A05, 05A15, 05B45
Keywords: diagonal placement, maximum independent set, constrained optimization 
@article{JIS_2017__20_2_a2,
     author = {Boyland,  Peter and Pint\'er,  Gabriella and Lauk\'o,  Istv\'an and Roth,  Ivan and Schoenfield,  Jon E. and Wasielewski,  Stephen},
     title = {On the maximum number of non-intersecting diagonals in an array},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {2},
     zbl = {1352.05007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a2/}
}
TY  - JOUR
AU  - Boyland,  Peter
AU  - Pintér,  Gabriella
AU  - Laukó,  István
AU  - Roth,  Ivan
AU  - Schoenfield,  Jon E.
AU  - Wasielewski,  Stephen
TI  - On the maximum number of non-intersecting diagonals in an array
JO  - Journal of integer sequences
PY  - 2017
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a2/
LA  - en
ID  - JIS_2017__20_2_a2
ER  - 
%0 Journal Article
%A Boyland,  Peter
%A Pintér,  Gabriella
%A Laukó,  István
%A Roth,  Ivan
%A Schoenfield,  Jon E.
%A Wasielewski,  Stephen
%T On the maximum number of non-intersecting diagonals in an array
%J Journal of integer sequences
%D 2017
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a2/
%G en
%F JIS_2017__20_2_a2
Boyland,  Peter; Pintér,  Gabriella; Laukó,  István; Roth,  Ivan; Schoenfield,  Jon E.; Wasielewski,  Stephen. On the maximum number of non-intersecting diagonals in an array. Journal of integer sequences, Tome 20 (2017) no. 2. http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a2/