An (n4) configuration is a family of n points and n (straight) lines in the Euclidean plane such that each point is on precisely four of the lines, and each line contains precisely four of the points. A configuration is said to be connected if it is possible to reach every point starting from an arbitrary point and stepping to other points only if they are on one of the lines of the configurati...

Given a set V of elements, S a family of subsets of V , and G a connected graph on vertex set S,a connected set cover (CSC) is a subfamily R of S such that every element in V is covered by at least one set of R, and the subgraph G[R] of G induced by R is connected. If furthermore G[R] is k-connected and every element in V is covered by at least m sets inR, thenR is a (k,m)-CSC. In this paper, w...

A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are now consistent with the existing results on connected dominating set problem which is a special case of the minimum connected set cover problem.

We completely describe the higher secant dimensions of all connected homogeneous projective varieties of dimension at most 3, in all possible equivariant embeddings. In particular, we calculate these dimensions for all Segre-Veronese embeddings of P1 × P1, P1 × P1 × P1, and P2 × P1, as well as for the variety F of incident point-line pairs in P2. For P2 × P1 and F the results are new, while the...

DEFINITION: Given a set of points p1, p2, ......., pn, the skyline query returns a set of points P, called as the skyline points, such that any point pi ∈ P is not dominated by any other point in the dataset. A point p1 dominates another point p2, if p1 is not worse than p2 in all dimensions and p1 is better than p2 in at least one dimension. In other words, a point p1 dominates another point p...

The topic is the average order A(G) of a connected induced subgraph graph G. This generalizes, to graphs in general, subtree tree. In 1983 Jamison proved that order, over all trees n, minimized by path Pn, being A(Pn)=(n+2)/3. 2018, Kroeker, Mol, and Oellermann conjectured Pn minimizes G - conjecture was recently proved. this short note we show lower bound can be improved if connectivity known....