In this paper, motivated by the study of the wide diameter and the Rabin number of graphs, we define the generalized k-diameter of k-connected graphs, and show that every k-regular k-connected graph on n vertices has the generalized k-diameter at most n/2 and this upper bound cannot be improved when n = 4k − 6 + i(2k − 4).

We demonstrate that ` rounds of the Sherali-Adams hierarchy and 2` rounds of the Lovász-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in `-layered graphs from Ω( √ k) to O(` · log k) where k is the number of terminals. This is an improvement over Rothvoss’ result that 2` rounds of the considerably stronger Lasserre SDP hierarchy r...

Objective: Evaluate the nutrient concentration at foliar level of chrysanthemums grown in tezontle sand using three concentrations Steiner Universal Nutrient Solution.
 Design/Methodology/Approach: A completely randomized design was used, each treatment represented a solution and had 11 repetitions, study variables were: nutrients: N, P, K, Ca, Mg S, plant height (AP), stem diameter (DT), ...

In this paper, we study the prize-collecting $k$ -Steiner tree ( xmlns:xlink="http://www.w3.org/1999/xlink">$\mathsf{PC}k\mathsf{ST}$ ) problem. We are given a graph xmlns:xlink="http://www.w3.org/1999/xlink">$G=(V, E)$ and an integer . The is connected undirected. A vertex xmlns:xli...

13. Chiasson, J-L. & Cherrington, A. D. (1983) in Glucagon I , (Lefebvre, P. ed.), pp. 361-382, Springer-Verlag, Berlin 14. Frizzell, R. T., Hendrick, G . K., Biggers, D. W., Lacy, D. B., Donahue, D. P., Green, D. R., Carr, R. K., Williams, P. E., Stevenson, R. W. & Cherrington, A. D. (1987) Gluconeogenesis plays the major role in sustaining glucose production during hypoglycemia in response to...

Strictly Chordality-k graphs (SCk) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For k ≥ 5, the study has been recently initiated in [1] and various structural and algorithmic results are reported. In this paper, we show that ma...

Given a metric space on n points, an α-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of the induced subtree is within an α factor of the optimal Steiner tree cost for X. An α-approximate differentially private algorithm for the Steiner tree problem takes...

We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V to optimality in O(B tw+2 · tw · |V |) time, where tw is the graph’s treewidth and the Bell number Bk is the number of partitions of a k-element set. This is a linear time algorithm for graphs with fixed treewidth and a polynomial algorithm for tw = O(log |V |/ log log |V |). While being faster than the ...