Combined algebraic properties of central* sets.
Comment construire un graphe PERT minimal
Common consequents in directed graphs
Common -transversal of finite families.
Common Transversals Of Finite Families
Common transversals of finite families.
Commutative subloop-free loops
We describe, in a constructive way, a family of commutative loops of odd order, , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group .
Commuting contractive families
A family f₁,..., fₙ of operators on a complete metric space X is called contractive if there exists a positive λ < 1 such that for any x,y in X we have for some i. Austin conjectured that any commuting contractive family of operators has a common fixed point, and he proved this for the case of two operators. We show that Austin’s conjecture is true for three operators, provided that λ is sufficiently small.
Commuting graphs for partially commutative nilpotent -groups of class 2.
Commuting involution graphs for 3-dimensional unitary groups.
Compact compatible topologies for graphs with small cycles.
Compact widths in metric trees
The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also...
Compactness properties of weighted summation operators on trees-the critical case
The aim of this paper is to provide upper bounds for the entropy numbers of summation operators on trees in a critical case. In a recent paper [Studia Math. 202 (2011)] we elaborated a framework of weighted summation operators on general trees where we related the entropy of the operator to those of the underlying tree equipped with an appropriate metric. However, the results were left incomplete in a critical case of the entropy behavior, because this case requires much more involved techniques....
Compactness properties of weighted summation operators on trees
We investigate compactness properties of weighted summation operators as mappings from ℓ₁(T) into for some q ∈ (1,∞). Those operators are defined by , t ∈ T, where T is a tree with partial order ⪯. Here α and σ are given weights on T. We introduce a metric d on T such that compactness properties of (T,d) imply two-sided estimates for , the (dyadic) entropy numbers of . The results are applied to concrete trees, e.g. moderately increasing, biased or binary trees and to weights with α(t)σ(t)...
Comparing a Cayley digraph with its reverse.
Comparing classification tree structures : a special case of comparing -ary relations
Comparing classification tree structures : a special case of comparing -ary relations II
Comparing classification tree structures: A special case of comparing q-ary relations II
Comparing q-ary relations on a set of elementary objects is one of the most fundamental problems of classification and combinatorial data analysis. In this paper the specific comparison task that involves classification tree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches to tree comparison are discussed in the context...
Comparing classification tree structures: a special case of comparing q-ary relations
Comparing q-ary relations on a set of elementary objects is one of the most fundamental problems of classification and combinatorial data analysis. In this paper the specific comparison task that involves classification tree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches to tree comparison are discussed in the context...
Comparing imperfection ratio and imperfection index for graph classes
Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs where the stable set polytope coincides with the fractional stable set polytope . For all imperfect graphs it holds that . It is, therefore, natural to use the difference between the two polytopes in order to decide how far an imperfect graph is away from being perfect. We discuss three...