منابع مشابه
Compatible geometric matchings
This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect matchings M and M ′ of the same set of n points, for some k ∈ O(log n), there is a sequence of perfect matchings M = M0,M1, . . . ,Mk = M , such that each Mi is compatible wi...
متن کاملMatchings in Geometric Graphs
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect if it matches all the vertices of the underling graph. A geometric matching is a matching in a geometric graph. In this thesis, we study matching problems in...
متن کاملGeometric Properties of Poisson Matchings
Suppose that red and blue points occur as independent Poisson processes of equal intensity in R, and that the red points are matched to the blue points via straight edges in a translation-invariant way. We address several closely related properties of such matchings. We prove that there exist matchings that locally minimize total edge length in d = 1 and d ≥ 3, but not in the strip R × [0, 1]. ...
متن کاملCompatible Matchings for Bichromatic Plane Straight-line Graphs
Two plane graphs with the same vertex set are compatible if their union is again a plane graph. We consider bichromatic plane straight-line graphs with vertex set S consisting of the same number of red and blue points, and (perfect) matchings which are compatible to them. For several different classes C of graphs, we present lower and upper bounds such that any given graph G(S) ∈ C admits a com...
متن کاملCounting perfect matchings of cubic graphs in the geometric dual
Lovász and Plummer conjectured, in the mid 1970’s, that every cubic graph G with no cutedge has an exponential in |V (G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3φ (G)|/72 distinct perfect matchings, where φ is the golden ratio. Our work builds on a novel approach relating Lovász and Plum...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2008
ISSN: 1571-0653
DOI: 10.1016/j.endm.2008.06.040