منابع مشابه
Bounding the Piercing Number
It is shown that for every k and every p ≥ q ≥ d + 1 there is a c = c(k, p, q, d) < ∞ such that the following holds. For every family H whose members are unions of at most k compact, convex sets in R in which any set of p members of the family contains a subset of cardinality q with a nonempty intersection there is a set of at most c points in R that intersects each member of H. It is also show...
متن کاملBounding cochordal cover number of graphs via vertex stretching
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...
متن کاملBounding the Security Number of a Graph
Given a graph G, the security number of G is the cardinality of a minimum secure set of G, the smallest set of vertices S ⊆ V (G) such that for all X ⊆ S, |N [X] ∩ S| ≥ |N [X] − S|. It is believed to be computationally difficult to find the security number of large graphs, so we present techniques for reducing the difficulty of both finding a secure set and determining bounds on the security nu...
متن کاملAbout the piercing number of a family of intervals
Given a universe (a set) U and a property P, (closed under inclusions, for subsets of U). Results of the type “if every subset of cardinality μ of a finite family F ⊂ U has property P, then the entire family F has property P”are called Helly type theorems. The minimum number μ for which the result is true is called the Helly number of the Helly-type theorem (U ,P , μ). In the case of Helly’s cl...
متن کاملBounding the Number of Plane Graphs
We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs is minimized when S is in convex position, and that the same result holds for several relevant subfamilies. In addition we construct a new extremal configuration, the so-called double zig-zag chain. Most noteworthy this example bears Θ∗( √ 7...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1995
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574042