Independent point-set dominating sets in graphs

AbstractLet P - {p1,p2,. . . ,pn} be an independent point-set in ℝd (i.e., there are no d + 1 on a hyperplane). A simplex determined by d + 1 different points of P is called empty if it contains no point of P in its interior. Denote the number of empty simplices in P by fd(P). Katchalski and Meir pointed out that . Here a random construction Pn is given with , where K(d) is a constant depending only on d. Several related questions are investigated.

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Independent point-set domination in line graphs

AKCE International Journal of Graphs and Combinatorics ◽

10.1080/09728600.2021.1995307 ◽

2021 ◽

pp. 1-6

Author(s):

Purnima Gupta ◽

Alka Goyal ◽

Ranjana Jain

Keyword(s):

Line Graphs ◽

Independent Point ◽

Point Set

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Characterizing minimal point set dominating sets

AKCE International Journal of Graphs and Combinatorics ◽

10.1016/j.akcej.2016.07.003 ◽

2016 ◽

Vol 13 (3) ◽

pp. 283-289 ◽

Cited By ~ 1

Author(s):

Purnima Gupta ◽

Rajesh Singh ◽

S. Arumugam

Keyword(s):

Dominating Sets ◽

Minimal Point ◽

Point Set

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On determining the independent point set for doubly periodic arrays and encoding two-dimensional cyclic codes and their duals

IEEE Transactions on Information Theory ◽

10.1109/tit.1981.1056396 ◽

1981 ◽

Vol 27 (5) ◽

pp. 556-565 ◽

Cited By ~ 45

Author(s):

S. Sakata

Keyword(s):

Cyclic Codes ◽

Two Dimensional ◽

Independent Point ◽

Periodic Arrays ◽

Point Set

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ON 2-POINT-SET DOMINATING SETS

Advances and Applications in Discrete Mathematics ◽

10.17654/dm021020139 ◽

2019 ◽

Vol 21 (2) ◽

pp. 139-162

Author(s):

Salma L Naga-Marohombsar ◽

Ferdinand P. Jamil

Keyword(s):

Dominating Sets ◽

Point Set

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

1996 ◽

Vol 54 ◽

pp. 440-441

Author(s):

P.J. Phillips ◽

J. Huang ◽

S. M. Dunn

Keyword(s):

Planar Graph ◽

Efficient Algorithm ◽

Spatial Organization ◽

Spatial Arrangement ◽

Stereo Image ◽

Image Model ◽

Geometric Invariants ◽

Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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Almost empty polygons

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.40.2003.3.1 ◽

2003 ◽

Vol 40 (3) ◽

pp. 269-286 ◽

Cited By ~ 4

Author(s):

H. Nyklová

Keyword(s):

Exact Results ◽

Point Sets ◽

Planar Point ◽

Convex Position ◽

Vertex Set ◽

Point Set ◽

Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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