On the perfect matching of disjoint compact sets by noncrossing line segments in Rn

Hosono, Kiyoshi; Matsuda, Katsumi

doi:10.1016/s0166-218x(01)00209-8

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2003

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Cited by 2 publications

(3 citation statements)

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“…See the article by O'Rourke [10] for a comprehensive overview. Several papers present results on the combinatorial structure of the visibility graph of line segments [12,3,9,8]. This paper builds upon the result of Hosono et al [7] that the visibility graph of a set of translates of the same convex polygon in IR 2 contains a Hamiltonian path.…”

Section: Introductionmentioning

confidence: 92%

The visibility graph of congruent discs is Hamiltonian

Rappaport

2003

Computational Geometry

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Section: Introductionmentioning

confidence: 92%

The visibility graph of congruent discs is Hamiltonian

Rappaport

2003

Computational Geometry

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“…Some results on the combinatorial structure of the visibility graph of line segments can be found in [1,2,4,6,8].…”

Section: Introductionmentioning

confidence: 99%

“…In [4] the notion of set of f -equal width objects is introduced. Let s denote a compact object in IR 2 .…”

Section: Introductionmentioning

confidence: 99%

Tight Bounds for Visibility Matching of f-Equal Width Objects

Rappaport

2003

Discrete and Computational Geometry

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Abstract. Let s denote a compact convex object in IR 2 . The f-width of s is the perpendicular distance between two distinct parallel lines of support of s with direction f . A set of disjoint convex compact objects in IR 2 is of equal f -width if there exists a direction f such that every pair of objects have equal f -width. A visibility matching, for a set of equal f -width objects is a matching using non-crossing lines of site in the visibility graph of the set. In this note we establish tight bounds on the size of a maximal visibility matching for a set of f -equal width objects by showing that 2n 3 ≤ h(n) ≤ 2n 3 .

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On the perfect matching of disjoint compact sets by noncrossing line segments in Rn

Cited by 2 publications

References 6 publications

The visibility graph of congruent discs is Hamiltonian

The visibility graph of congruent discs is Hamiltonian

Tight Bounds for Visibility Matching of f-Equal Width Objects

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