We consider the problem (MSSS) of nding a strongly connected spanning subgraph with the minimum number of arcs in a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamil-tonian cycle problem. We show that the problem is polynomially solvable for quasi-transitive digraphs. We describe the minimum number of arcs in such a spanning subgraph of a qu...

We describe algorithms for finding shortest paths and distances in a planar digraph which exploit the particular topology of the input graph. We give both sequential and parallel algorithms that work on a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. For outerplanar digraphs, for instance, the data structures can be updated after any such change in o...

We begin with some terminology. All digraphs in this paper are finite. For a digraph G, we denote its vertex and edge sets by V (G) and E(G), respectively. Unless otherwise stated, we assume |V (G)| = n. The members of E(G) are ordered pairs of vertices. We use the notation uv to denote an ordered pair of vertices (u, v) (whether or not u and v are adjacent). We only consider digraphs which hav...

Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a, b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.

The traditional parameter used as a measure of vulnerability of a network modeled by a graph with perfect nodes and edges that may fail is the edge connectivity λ. Of course , () p q K p λ = where p q ≤. In that case, failure of the network simply means that the surviving subgraph becomes disconnected upon the failure of individual edges. If, instead, failure of the network is defined to mean t...

Let G be a graph with odd edge-connectivity r. It is proved in this paper that if r > 3, then G has a 3-cycle (1, 2)-cover of total length at most ((r + 1)|E(G)|)/r . © 2005 Elsevier B.V. All rights reserved.

In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...

Given a connected graph $$G = (V, E)$$ , we seek to partition the vertex set V into k non-empty parts such that subgraph induced by each part is connected, and maximally balanced in way maximum cardinality of these minimized. We refer this problem as min-max denote it -BGP. The vertex-weighted version on trees has been studied since about four decades ago, which admits linear time exact algorit...

Article history: Received 17 January 2008 Available online 21 March 2012