An (r, `)-partition of a graph G is a partition of its vertex set into r independent sets and ` cliques. A graph is (r, `) if it admits an (r, `)-partition. A graph is well-covered if every maximal independent set is also maximum. A graph is (r, `)-well-covered if it is both (r, `) and well-covered. In this paper we consider two different decision problems. In the (r, `)-Well-Covered Graph prob...

We prove that there is ǫ > 0 and p0 > 0 such that for every prime p > p0, every subset S of Z/pZ which satisfies |2S| ≤ (2 + ǫ)|S| and 2(|2S|) − 2|S| + 3 ≤ p is contained in an arithmetic progression of length |2S| − |S| + 1. This is the first result of this nature which places no unnecessary restrictions on the size of S.

A graph is well covered if every maximal independent set has the same size and very well covered if every maximal independent set contains exactly half the number of vertices. In this paper, we present an alternative characterization of a certain sub-class of well-covered graphs and show that this generalizes a characterization of very well covered graphs given by Favaron 3].

CONTEXT In India, 14% of the population use smoked tobacco products. Increasing prices of these products is one of the measures to curb their consumption. AIMS This study analyzes "unit price" and "daily consumption" of cigarettes and bidis and investigates their relation with each other. SETTINGS AND DESIGN A cross-sectional survey was conducted in four states of India (Bihar, West Bengal,...

Given a commodity available at different prices, a unit-price account of choice predicts preference for the cheaper alternative. This experiment determined if rhesus monkeys preferred remifentanil (an ultra-short-acting micro-opioid agonist) delivered at a lower unit price over a higher-priced remifentanil alternative (Phases 1 and 3). Choice between equal-priced alternatives also was assessed ...

This study were estimated the contribution of carcass traits to unit price, to analyze the marbling score as a categorical variable rather than a numerical variable, and to develop an optimal model that also includes the holiday effect and the raising period. The data for this study were acquired from the Quality Evaluation of the Korea Institute for Animal Products, and consisted of the tradin...

Key pecking by 3 pigeons was maintained by a multiple fixed-ratio 10, fixed-ratio 30, fixed-ratio 90 schedule of food presentation. Components differed with respect to amount of reinforcement, such that the unit price was 10 responses per 1-s access to food. Acute administration of morphine, l-methadone, and cocaine dose-dependently decreased overall response rates in each of the components. Wh...

A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...