We first define the notion of approximation chain and then we use it to obtain, in polynomial time, asymptotic approximation ratio of min{κ/μ, [κ′ log(log ∆)]/∆} (where κ is a fixed positive constant, κ′ is a constant depending on κ, and ∆, μ are the maximum and the average degrees of the graph, respectively). This result essentially improves, from both complexity and approximation quality poin...

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

in this note we are going to survey several invariants of finite groups related either to their orders or to generating sets or to lattices of subgroups. some relations among these invariants will be exhibited. special attention will be paid to monotonicity of them.

We show that every (sub)cubic n-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978 which implies that it contains an independent set of size at least 0.4352n. Our bound on the independence number is valid to random cubic graphs as well as it improves existing lower bounds on the maximum cut in cubic graphs with large girth.

We introduce a quadratic programming framework on graphs (which incorporates MAXIMUM-CUT and MAXIMUM-INDEPENDENT-SET) and show that problems which are expressible in the framework can be solved in polynomial time on graphs without long odd cycles.

Consider a family of chords i n a c ircle . is obtained by representing each chord by a vertex, two vertices being connected by an edge when the corresponding chords intersect. I n t h i s paper, we describe e f f i c i en t algorithms for finding a ma3cimwn clique and a maximum independent s e t of circle graphs. the number of vertices i n the graph. Key WO&: Circle graph, transi t ive graph, ...

Let G be a k-degenerate graph of order n. It is well-known that G has no more edges than Sn,k, the join of a complete graph of order k and an independent set of order n−k. In this note, it is shown that Sn,k is extremal for some spectral parameters of G as well. More precisely, letting μ (H) and q (H) denote the largest eigenvalues of the adjacency matrix and the signless Laplacian of a graph H...

We explore the structure of the maximum vertex independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. At the same time, we will consider benzenoids: plane graphs with hexagonal faces and one large outer face. In the case of fullerenes, a maximum vertex independence set may constructed as follows: (i) Pair up the pentagonal faces. (ii) Delete the edges of a ...