scholarly journals On the geodetic Radon number of grids

2013 ◽  
Vol 313 (1) ◽  
pp. 111-121 ◽  
Author(s):  
Mitre Costa Dourado ◽  
Dieter Rautenbach ◽  
Vinícius Gusmão Pereira de Sá ◽  
Jayme Luiz Szwarcfiter
Keyword(s):  
Radon Number

Polynomial time algorithm for the Radon number of grids in the geodetic convexity

2013 ◽  
Vol 44 ◽  
pp. 371-376
Author(s):  
Mitre Costa Dourado ◽  
Dieter Rautenbach ◽  
Vinícius Gusmão Pereira de Sá ◽  
Jayme Luiz Szwarcfiter
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Radon Number

Algorithmic and structural aspects of the P 3-Radon number

2013 ◽  
Vol 206 (1) ◽  
pp. 75-91 ◽  
Author(s):  
Mitre C. Dourado ◽  
Dieter Rautenbach ◽  
Vinícius Fernandes dos Santos ◽  
Philipp M. Schäfer ◽  
Jayme L. Szwarcfiter ◽  
...  
Keyword(s):  
Radon Number ◽  
Structural Aspects

scholarly journals Radon Numbers Grow Linearly

2021 ◽  
Author(s):  
Dömötör Pálvölgyi
Keyword(s):  
Convex Hulls ◽  
Convexity Space ◽  
Helly Theorem ◽  
Radon Number

AbstractDefine the k-th Radon number $$r_k$$ r k of a convexity space as the smallest number (if it exists) for which any set of $$r_k$$ r k points can be partitioned into k parts whose convex hulls intersect. Combining the recent abstract fractional Helly theorem of Holmsen and Lee with earlier methods of Bukh, we prove that $$r_k$$ r k grows linearly, i.e., $$r_k\le c(r_2)\cdot k$$ r k ≤ c ( r 2 ) · k .

Star-shape, Radon number, and minty graphs

Cybernetics ◽  
1987 ◽  
Vol 23 (2) ◽  
pp. 147-153
Author(s):  
L. F. German ◽  
O. I. Topale
Keyword(s):  
Radon Number

scholarly journals An upper bound on the P3-Radon number

2012 ◽  
Vol 312 (16) ◽  
pp. 2433-2437 ◽  
Author(s):  
Mitre C. Dourado ◽  
Dieter Rautenbach ◽  
Vinícius Fernandes dos Santos ◽  
Philipp M. Schäfer ◽  
Jayme L. Szwarcfiter ◽  
...  
Keyword(s):  
Upper Bound ◽  
Radon Number

scholarly journals On Weak $$\epsilon $$-Nets and the Radon Number

2020 ◽  
Vol 64 (4) ◽  
pp. 1125-1140
Author(s):  
Shay Moran ◽  
Amir Yehudayoff
Keyword(s):  
Radon Number ◽  
Epsilon Nets

Some Steiner concepts on lexicographic products of graphs

2014 ◽  
Vol 06 (04) ◽  
pp. 1450060 ◽  
Author(s):  
Bijo S. Anand ◽  
Manoj Changat ◽  
Iztok Peterin ◽  
Prasanth G. Narasimha-Shenoi
Keyword(s):  
Steiner Tree ◽  
Steiner Trees ◽  
Partial Answer ◽  
Lexicographic Product ◽  
Complete Answer ◽  
Radon Number ◽  
Minimum Number ◽  
Carathéodory Number ◽  
Product Of Graphs

Let G be a graph and W a subset of V(G). A subtree with the minimum number of edges that contains all vertices of W is a Steiner tree for W. The number of edges of such a tree is the Steiner distance of W and union of all vertices belonging to Steiner trees for W form a Steiner interval. We describe both of these for the lexicographic product of graphs. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number.

scholarly journals Near-linear-time algorithm for the geodetic Radon number of grids

2016 ◽  
Vol 210 ◽  
pp. 277-283 ◽  
Author(s):  
Mitre Costa Dourado ◽  
Vinícius Gusmão Pereira de Sá ◽  
Dieter Rautenbach ◽  
Jayme Luiz Szwarcfiter
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Radon Number

scholarly journals Open packing, total domination, and theP3-Radon number

2013 ◽  
Vol 313 (9) ◽  
pp. 992-998 ◽  
Author(s):  
Michael A. Henning ◽  
Dieter Rautenbach ◽  
Philipp M. Schäfer
Keyword(s):  
Total Domination ◽  
Radon Number ◽  
Open Packing

On the Radon Number for P 3-Convexity

2012 ◽  
pp. 267-278 ◽  
Author(s):  
Mitre C. Dourado ◽  
Dieter Rautenbach ◽  
Vinícius Fernandes dos Santos ◽  
Philipp M. Schäfer ◽  
Jayme L. Szwarcfiter ◽  
...  
Keyword(s):  
Radon Number
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