Let G be a graph. The Steiner distance of $$W\subseteq V(G)$$ is the minimum size connected subgraph containing W. Such necessarily tree called W-tree. set $$A\subseteq k-Steiner general position if $$V(T_B)\cap A = B$$ holds for every $$B\subseteq A$$ cardinality k, and B-tree $$T_B$$ . number $$\mathrm{sgp}_k(G)$$ largest in G. cliques are introduced used to bound from below. determined trees...

For a graph G = ( V , E ) and set S ⊆ of size at least 2, an S-Steiner tree T is subgraph that with . Two -Steiner trees ′ are internally disjoint (resp. edge-disjoint if ∩ ∅ ). Let κ λ denote the maximum number edge-disjoint) in The k-tree connectivity k edge-connectivity then defined as minimum ), where ranges over all -subsets In Li et al. (2018) [12] authors conjectured connected has vertic...

A combinatorial characterization of resolvable Steiner 2-(v, k, 1) designs embeddable as maximal arcs in a projective plane of order (v − k)/(k − 1) is proved, and a generalization of a conjecture by Andries Brouwer [9] is formulated.

We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V, E) with edge costs, a collection D ⊆ V × V of ordered node pairs, and an integer k ≤ |D|, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems ar...

In this paper, we present an exact algorithm for the Steiner tree problem. The algorithm is based on certain pre-computed index structures. Our algorithm offers a practical solution for the Steiner tree problems on graphs of large size and bounded number of terminals.

In this paper, we determine the spectrum (the set of all possible volumes) of simple (v, 3, 2) trades for any fixed foundation size v 6≡ 5 (mod 6). Index Words: trades, spectrum, Steiner triple systems, large sets of Steiner triple systems MR Subject Classification: 05B07, 05B05