Results 301 to 310 of about 8,223,452 (320)
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Combinatorica, 1990
A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of ...
T. Bisztriczky, G. Fejes Tóth
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A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of ...
T. Bisztriczky, G. Fejes Tóth
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Independent Gödel sentences and independent sets
Journal of Symbolic Logic, 1975In this paper we investigate some of the recursion-theoretic problems which are suggested by the logical notion of independence.A set S of natural numbers will be said to be k-independent (respectively, ∞-independent) if, roughly speaking, in every correct system there is a k-element set (respectively, an infinite set) of independent true sentences of ...
Dawes, A. M., Florence, J. B.
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1999
Abstract A subset S ⊆V in a TS(v, λ) (V,B)is independentif B ⊈Sfor all BE B.An independent set is maximalif, for all x∈ V\ S, S⋃ ( x) is not independent (that is, it is maximal with respect to set inclusion). It is maximumif it has the largest cardinality of any independent set in the design.
Charles J Colbourn, Alexander Rosa
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Abstract A subset S ⊆V in a TS(v, λ) (V,B)is independentif B ⊈Sfor all BE B.An independent set is maximalif, for all x∈ V\ S, S⋃ ( x) is not independent (that is, it is maximal with respect to set inclusion). It is maximumif it has the largest cardinality of any independent set in the design.
Charles J Colbourn, Alexander Rosa
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Finding a Maximum Independent Set
SIAM Journal on Computing, 1977We present an algorithm which finds a maximum independent set in an n-vertex graph in 0($2^{n/3}$) time. The algorithm can thus handle graphs roughly three times as large as could be analyzed using a naive algorithm.
Tarjan, Robert Endre +1 more
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1998
Abstract The line graph of G is a graph L whose vertices are edges of G. Two vertices are neighbors in L if they have a common endpoint (as edges) in G. Then a set M of edges of G is a matching in G iff it is independent (as a set of vertices) in L.
Marek Karpinski, Wojciech Rytter
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Abstract The line graph of G is a graph L whose vertices are edges of G. Two vertices are neighbors in L if they have a common endpoint (as edges) in G. Then a set M of edges of G is a matching in G iff it is independent (as a set of vertices) in L.
Marek Karpinski, Wojciech Rytter
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On Dominating Sets and Independent Sets of Graphs
Combinatorics, Probability and Computing, 1999For a graph G on vertex set V = {1, …, n} let k = (k1, …, kn) be an integral vector such that 1 [les ] ki [les ] di for i ∈ V, where di is the degree of the vertex i in G. A k-dominating set is a set Dk ⊆ V such that every vertex i ∈ V[setmn ]Dk has at least ki neighbours in Dk.
Harant, Jochen +2 more
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2013
An independent set of a graph is a subset of its vertices such that there are not any two adjacent vertices in this set. Finding the maximal independent set of a graph has many important applications such as clustering in wireless networks, and independent sets can also be used to build other graph structures.
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An independent set of a graph is a subset of its vertices such that there are not any two adjacent vertices in this set. Finding the maximal independent set of a graph has many important applications such as clustering in wireless networks, and independent sets can also be used to build other graph structures.
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