Let G be a simple undirected graph of order n. For an independent set S C V(G) of k vertices, we define the k neighborhood intersections S, = { u E V(G)\SIIN(u) n Sl = 11, 1 5 ir k, with s; = ISJ. Using the concept of insertible vertices and the concept of neighborhood intersections, we prove the following theorem. Theorem. Let G be a graph of order n and connectivity K 2 2. Then G is hamiltoni...

We provide a probabilistic analysis of the second order term that arises in path-following algorithms for linear programming. We use this result to show that two such methods, algorithms generating a sequence of points in a neighborhood of the central path and in its relaxation , require a worst-case number of iterations that is O(nL) and an anticipated number of iterations that is O(log(n)L). ...

A (proper) coloring of a finite simple graph (G) is pe#ect if it uses exactly o(G) colors, where o(G) denotes the order of a largest clique in G. A coloring is locally-perfect [3] if it induces on the neighborhood of every vertex v a perfect coloring of this neighborhood. A graph G is perfect (resp. locally-petfect) if every induced subgraph admits a perfect (resp. locally-perfect) coloring. Pr...

in this paper, the concept of {sl local base with  stratifiedstructure} in $i$-topological vector spaces is introduced. weprove that every $i$-topological vector space has a balanced localbase with stratified structure. furthermore, a newcharacterization of $i$-topological vector spaces by means of thelocal base with stratified structure is given.

We can construct the neighborhood complex N(G), with vertices v1, ..., vn, from the graph G, in such a way that, for each vertex v of G, there is a simplex containing the vertex v along with its neighbouring vertices, corresponding to the directed edges v → w. To construct this, we can take each vertex in v1, ..., vn one by one, and construct the simplex along with it’s neighbors, each time. Th...

(1.3) M = M1 ∪M2 , M1 ∩M2 = Y = ∂M1 = ∂M2 . In this paper, we study the adiabatic decomposition of the ζ-determinant of D2, which describes the contributions in detζD coming from the submanifolds M1 and M2. Throughout the paper, we assume that the manifold M and the operator D have product structures in a neighborhood of the cutting hypersurface Y . Hence, there is a bicollar neighborhood N ∼= ...

sports spaces are the most important services in the city, that have a significant role in raising physical and mental health citizens. after studying the existing sports spaces in the neighborhood, district, region and city of zanjan, determined levels and percapita sport spaces of zanjan city. a total of 19 spaces sports zanjan city, 9 sport spaces neighborhood-scale, 6 sport spaces district ...

A corpus of 5,765 consonant-vowel-consonant sequences (CVCs) was compiled, and phonotactic probability and neighborhood density were computed for both child and adult corpora. This corpus of CVCs, provided as supplementary materials, was analyzed to address the following questions: (1) Do computations based on a child corpus differ from those based on an adult corpus? (2) Do the phonotactic pro...