نتایج جستجو برای: connected set
تعداد نتایج: 762050 فیلتر نتایج به سال:
In the sequel, we suppose that p(l) = 2, p(2), p(3),... is the sequence of primes in ascending order. Let T be a rooted tree, r its root. The connected components of Tr are denoted by T, ,..., T,, where v is the degree of r. The graphs Tj ul,..., v) obviously are trees, which we transform into rooted trees by defining as the root of Tj the vertex of 7” which is adjacent to r in T. We now assign...
Let S be a subset of R with finite positive Lebesgue measure. The Beer index of convexity b(S) of S is the probability that two points of S chosen uniformly independently at random see each other in S. The convexity ratio c(S) of S is the Lebesgue measure of the largest convex subset of S divided by the Lebesgue measure of S. We investigate the relationship between these two natural measures of...
Lemma 1. f is submodular function. Proof. Let X, Y, Z ⊆ V , and u, v ∈ V be X = Z ∪ {u}, Y = Z ∪ {v}, v ∈ V , and e′(v) be the number of outgoing edges of u toward any vertices of Z. Let m be the number of connected components which are connected to u, but not connected to Z and b, and n be the number of connected components which are connected to v, but not connected to Z and u. 1. There are n...
Let r be the fundamental group of a hyperbolic surface of genus g; for I ::; p ::; q, PSU(p, q) is the group of isometries of a certain Hermitian symmetric space Dp , q of rank p. There exists a characteristic number c : Hom(r, PSU(p, q)) --+ lR, which is constant on each connected component and such that Ic(p)1 ::; 4pn(g I) for every representation p. We show that representations with maximal ...
We prove that given two metrics g+ and g− with curvature κ < −1 on a closed, oriented surface S of genus τ ≥ 2, there exists an AdS manifold N with smooth, space-like, strictly convex boundary such that the induced metrics on the two connected components of ∂N are equal to g+ and g−. Using the duality between convex space-like surfaces in AdS3, we obtain an equivalent result about the prescript...
Consider an asymmetric wireless network represented by a digraph G = (V , E). A subset of vertices U is called a strongly connected dominating set (SCDS) if the subgraph induced by U is strongly connected and every vertex not in U has both an in-neighbor in U and an out-neighbor in U . SCDS plays an important role of the virtual backbone in asymmetric wireless networks. Motivated by the constru...
We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. We show that there is a transitive group action on this set. Thus such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. We also obtain a description of the set of these varieties that are zero-d...
Let B be a building over a type set I . Suppose J ⊆ I meets every connected component of the diagram of B and let (P,L) be the point-line truncation of the J -Grassmann geometry of B. We present a theorem that allows one to identify shadows of apartments of residues of B in the point-collinearity graph of (P,L). Also, other results related to shadows of apartments of residues and shadows of res...
The problem of packing k vertex-disjoint copies of a graph H into another graph G is NP-complete if H has more than two vertices in some connected component. In the framework of parameterized complexity we analyze a particular family of instances of this problem, namely the packing of stars. We prove that packing k copies of H = K1,s is fixed-parameter tractable and give a quadratic kernel for ...
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