منابع مشابه
The Caratheodory number for the k-core
Here and in what follows we assume S is a finite multiset in R d. This means tha t the points in S have "multiplicity". Strict ly speaking, a multiset is a map S : F --, R d and in our case F is finite. Then corekS = M{convS(E) : E C_ F, IF \ El _< k}. From now on we do not say explicitly tha t the sets in question are multisets. This will make the no ta t ion simpler and will not cause confusi...
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In many network applications nodes are stable provided they have at least k neighbours, and a network of k-stable nodes is called a k-core. The vulnerability to random attack is characterized by the size of culling avalanches which occur after a randomly chosen k-core node is removed. Simulations of lattices in two, three and four dimensions, as well as small-world networks, indicate that power...
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The physics of k-core percolation pertains to those systems whose constituents require a minimum number of k connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from orientational ordering in solid ortho-para H2 mixtures to the onset of rigidity in barjoint networks to dynamical arrest in glass-forming liquids. Unlike ordinary (k=1...
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We investigate in this paper the set of kadditive capacities dominating a given capacity, which we call the k-additive core. We study its structure through achievable families, which play the role of maximal chains in the classical case (k = 1), and show that associated capacities are elements (possibly a vertex) of the k-additive core when the capacity is (k+1)-monotone. As a particular case, ...
متن کاملThe k-Core and Branching Processes
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold λc for the emergence of a non-trivial k-core in the random graph G(n, λ/n), and the asymptotic size of the k-core above the threshold. We give a new proof of this result using a local coupling of the graph to a suitable branching process. This proof ext...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2013
ISSN: 1556-5068
DOI: 10.2139/ssrn.2344752