It is proved that there are triangle-free intersection graphs of line segments in the plane with arbitrarily small ratio between the maximum size of an independent set and the total number of vertices.

Over the past few years, our institution has been in the process of rethinking the structure of our College of Business curriculum. This is motivated by three major factors: Demands of industry for the inclusion of “soft skills” in our curriculum, the recent emphasis by AACSB on assessment of student learning, and dissatisfaction with the performance of the core MIS course. This paper describes...

A graph is called well-covered if every maximal independent set of vertices of G is a maximum independent set; recall that S is independent if no two of its vertices are adjacent. In this paper we define the concept of well-covered by monochromatic paths graphs which is a variation of well-covered graphs. We consider some classical constructions of graphs: G-join of graphs and duplication of a ...

This paper investigates output-size sensitiveness of construction of OBDD by analyzing the maximal independent set problem of a graph, which would give several insights to e cient manipulation of Boolean functions by OBDD and graph theory.

The independence polynomial i(G, x) of a graph G is the generating function of the numbers of independent sets of each size. A graph of order n is very well-covered if every maximal independent set has size n/2. Levit and Mandrescu conjectured that the independence polynomial of every very well-covered graph is unimodal (that is, the sequence of coefficients is nondecreasing, then nonincreasing...

We investigate sufficient conditions, and in case that D be an asymmetrical digraph a necessary and sufficient condition for a digraph to have the following property: “In any induced subdigraph H of D, every maximal independent set meets every non-augmentable path”. Also we obtain a necessary and sufficient condition for any orientation of a graph G results a digraph with the above property. Th...

Suppose that n processors are arranged in a ring and can communicate only with their immediate neighbors. We show that any probabilistic algorithm for 3 coloring the ring must take at least 1 2 log n 2 rounds, otherwise the probability that all processors are colored legally is less than 1 2 . A similar time bound holds for selecting a maximal independent set. The bound is tight (up to a consta...

Let k be a positive integer and G = (V (G), E(G)) a graph. A subset S of V (G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k − 1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). In this paper, we study the properties of graphs for which the k-independence number changes whenever an edge or vertex is ...

Let G be a graph with n vertices, with independence number α, and with with no Kt+1-minor for some t ≥ 5. It is proved that (2α− 1)(2t − 5) ≥ 2n− 5.

In this paper we will define a cardinal invariant corresponding to the independence number for partitions of ω. By using Cohen forcing we will prove that this cardinal invariant is consistently smaller than the continuum.