On the dual Helly number and irreducible decompositions of the unit in lattices

1993 ◽  
Vol 54 (3) ◽  
pp. 899-902
Author(s):  
A. P. Zolotarev
Keyword(s):  
Helly Number

A helly-number fork-almost-neighborly sets

1972 ◽  
Vol 11 (4) ◽  
pp. 347-348 ◽  
Author(s):  
Marilyn Breen
Keyword(s):  
Helly Number

scholarly journals A helly number for unions of two boxes inR2

1985 ◽  
Vol 8 (2) ◽  
pp. 267-273 ◽  
Author(s):  
Marilyn Breen
Keyword(s):  
Convex Sets ◽  
Helly Number ◽  
Boundary Points ◽  
Polygonal Region

LetSbe a polygonal region in the plane with edges parallel to the coordinate axes. If every5or fewer boundary points ofScan be partitioned into setsAandBso thatconv A⋃ conv B⫅S, thenSis a union of two convex sets, each a rectangle. The number5is best possible.Without suitable hypothesis on edges ofS, the theorem fails. Moreover, an example reveals that there is no finite Helly number which characterizes arbitrary unions of two convex sets, even for polygonal regions in the plane.

scholarly journals On the Computational Complexity of the Helly Number in the P3 and Related Convexities

2019 ◽  
Vol 346 ◽  
pp. 285-297
Author(s):  
Moisés T. Carvalho ◽  
Simone Dantas ◽  
Mitre C. Dourado ◽  
Daniel F.D. Posner ◽  
Jayme L. Szwarcfiter
Keyword(s):  
Computational Complexity ◽  
Helly Number

Maximal $S$-Free Convex Sets and the Helly Number

2016 ◽  
Vol 30 (4) ◽  
pp. 2206-2216 ◽  
Author(s):  
Michele Conforti ◽  
Marco Di Summa
Keyword(s):  
Convex Sets ◽  
Helly Number

Single bend paths on a grid have strong helly number 4: errata atque emendationes ad “edge intersection graphs of single bend paths on a grid”

Networks ◽  
2013 ◽  
Vol 62 (2) ◽  
pp. 161-163 ◽  
Author(s):  
Martin Charles Golumbic ◽  
Marina Lipshteyn ◽  
Michal Stern
Keyword(s):  
Intersection Graphs ◽  
Helly Number

scholarly journals On the Helly Number for Hyperplane Transversals to Unit Balls

2000 ◽  
Vol 24 (2) ◽  
pp. 171-176 ◽  
Author(s):  
B. Aronov ◽  
J. E. Goodman ◽  
R. Pollack ◽  
R. Wenger
Keyword(s):  
Helly Number

Involving the Helly number in Pareto reducibility

2008 ◽  
Vol 36 (2) ◽  
pp. 173-176 ◽  
Author(s):  
Nicolae Popovici
Keyword(s):  
Helly Number

A Tverberg-type generalization of the Helly number of a convexity space

1981 ◽  
Vol 16 (1) ◽  
pp. 117-125 ◽  
Author(s):  
Jean-Paul Doignon ◽  
John R. Reay ◽  
Gerard Sierksma
Keyword(s):  
Convexity Space ◽  
Helly Number
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