Article history: Received 22 February 2016 Available online 23 April 2017 Given a directed graph D = (V, E) with n vertices and a permutation π : V → V on its vertices, we say that π has a drop at a vertex u ∈ V is (u, π(u)) is an edge of D. Letting 〈 D k 〉 denote the number of permutations on V with precisely k drops, we can define the binomial drop polynomial BD(x) = ∑ k 〈 D k 〉( x+k n ) . In...

We study a signed variant of edge covers of graphs. Let b be a positive integer, and let G be a graph with minimum degree at least b. A signed b-edge cover of G is a function f : E(G) → {−1, 1} satisfying e∈EG(v) f(e) ≥ b for every v ∈ V (G). The minimum of the values of e∈E(G) f(e), taken over all signed b-edge covers f of G, is called the signed b-edge cover number and is denoted by ρb(G). Fo...

In this paper we show that the problem of identifying an edge (i, j) in a graph G such that there exists an optimal vertex cover S of G containing exactly one of the nodes i and j is NP-hard. Such an edge is called a weak edge. We then develop a polynomial time approximation algorithm for the vertex cover problem with performance guarantee 2 − 1 1+σ , where σ is an upper bound on a measure rela...

Forest fragmentation results in a loss of forest interior and an increase in edge habitat. We studied how understorey bird community composition and habitat variables changed along an edge-to-interior gradient in a 1248-ha lowland rainforest patch in peninsular Malaysia. Birds and environmental variables such as vegetation structure and litter depth were detected within a 25-m radius of each of...

We show that edge-clique graphs of cocktail party graphs have unbounded rankwidth. This, and other observations lead us to conjecture that the edge-clique cover problem is NP-complete for cographs. We show that the independent set problem on edge-clique graphs of cographs and of distance-hereditary graphs can be solved in polynomial time. We show that the independent set problem on edge-clique ...

Let G be a simple graph with vertex set and edge set   V G   E G . An edge coloring C of G is called an edge cover coloring, if each color appears at least once at each vertex   v V G  . The maximum positive integer k such that G has a k edge cover coloring is called the edge cover chromatic number of G and is denoted by . It is known that for any graph G,   c G    1 c G      ...

In cooperative games, a key question is to find a division of payoffs to coalition members in a fair manner. Nucleolus is one of such solution concepts that provides a stable solution for the grand coalition. We study the computation of the nucleolus of a number of cooperative games, including fractional matching games and fractional edge cover games on general weighted graphs, as well as verte...

Article history: Received 21 October 2013 Received in revised form 30 September 2014 Accepted 21 October 2014 Available online 28 October 2014 Communicated by G. Ausiello

We present eecient polynomial time algorithms that place bn=2c vertex guards which cover the surface of an n-vertex polyhedral terrain, and similarly, bn=3c edge guards which cover the surface of an n-vertex polyhedral terrain. The time complexity of both algorithms, dominated by the cost of nding a maximum matching in a graph, is O(n 3=2).

We initiate the algorithmic study of the following “structured augmentation” question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition of G and H with respect to injective mapping φ : V (H) → V (G) if every edge uv of F is either an edge of G, or φ−1(u)φ−1(v) is an edge of H. Thus F contain...