Disjoint Edges in Geometric Graphs
نویسندگان
چکیده
A geometric graph is a drawn in the plane so that its vertices and edges are represented by points general position straight line segments, respectively. vertex of called pointed if it lies outside convex hull neighbours. We show for with $$n$$ $$e$$ there at least $$\frac{n}{2}\left(\begin{array}{cc}2e/n\\3\end{array}\right)$$ pairs disjoint provided $$2e\ge n$$ all pointed. Besides, we prove any edge from most $$m$$ edges, then number this does not exceed $$n(\sqrt{1+8m}+3)/4$$ sufficiently large. These two results tight an infinite family graphs.
منابع مشابه
Disjoint Edges in Geometric Graphs
A stract. Answering an old question in com inatorial geometry, we show that any configuration consisting of a set V of n points in general position in the plane and a set of 6n-5 closed straight line segments whose endpoints lie in V, contains three pairwise disjoint line segments. A geometric graph is a pair G=(V, E), where V is a set of points (=vertices) in general position in the plane, i ....
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-022-02563-2