For a finite multigraph G, the reliability function of G is the probability RG(q) that if each edge of G is deleted independently with probability q then the remaining edges of G induce a connected spanning subgraph of G; this is a polynomial function of q. In 1992, Brown and Colbourn conjectured that for any connected multigraph G, if q ∈ C is such that RG(q) = 0 then |q| ≤ 1. We verify that t...

The tree width of a graph G measures how close G is to being a tree or a series-parallel graph. Many well-known problems that are otherwise NP-complete can be solved efficiently if the underlying graph structure is restricted to one of fixed tree width. In this paper we prove that the tree width of goto-free Ada programs without labeled loops is ≤ 6. In addition we show that both the use of got...

Wprowadzenie W powszechnym przekonaniu dla »adnego problemu NPtrudnego nie istnieje algorytm wielomianowy. Jednak»e wiele grafowych problemów NP-trudnych mo»emy rozwi¡za¢ w czasie wielomianowym dla wybranych klas grafów takich jak drzewa, grafy zewn¦trznie planarne czy te» grafy szeregowo-równolegae (ang. series-parallel). Szeroko±¢ drzewiasta (ang. treewidth) jest parametrem grafowym wprowadzo...

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) partially entangled bipartite pure states is generally benchmarked against the classical percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies new more effective mapping QN, referred ...

A mixed s-stack q-queue layout of a graph consists linear order its vertices and partition edges into s stacks q queues, such that no two in the same stack cross queue nest. In 1992, Heath Rosenberg conjectured every planar admits 1-stack 1-queue layout. Recently, Pupyrev disproved this by demonstrating partial 3-tree does not admit note, we strengthen Pupyrev's result showing conjecture hold e...