We study the problem of computing an equitable 2-fan for three masses distributed on the 2-sphere. The existence of an equitable 2-fan was shown by Bárány and Matoušek [3]. The contribution of this paper is two-fold. (i) We prove the existence of an infinite set of equitable 2-fans. (ii) We present an efficient algorithm for finding an equitable 2fan when the mass distributions are discrete, i....

An equitable k-coloring of a graph is defined by a partition of its vertices into k disjoint stable subsets, such that the difference between the cardinalities of any two subsets is at most one. The equitable coloring problem consists of finding the minimum value of k such that a given graph can be equitably k-colored. We present two new integer programming formulations based on representatives...

Maritime delimitation usually starts with the calculation of an equidistance line, which is often corrected for special circumstances. The correction process aims to produce a line that is “equitable”, a concept open to various interpretations. While the equidistance line is calculated by a technical expert, an equitable line is the result of a negotiation process. Technical support is, in that...

A subset D of V (G) is called an equitable dominating set of a graph G if for every v ∈ (V − D), there exists a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| 6 1. The minimum cardinality of such a dominating set is denoted by γe(G) and is called equitable domination number of G. In this paper we introduce the equitable edge domination and equitable edge domatic number in a graph, exact...

An equitable risk allocation between contracting parties plays a vital role in enhancing the performance of the project. This research presents a new quantitative risk allocation approach by integrating fuzzy logic and bargaining game theory. Owing to the imprecise and uncertain nature of players’ payoffs at different risk allocation strategies, fuzzy logic is implemented to determine the value...

In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper, we consider an equitable coloring of some corona products H G of two graphs G and H. In particular, we show that deciding the colorability of H G is NP-complete even if G is 4-regular and H is . 2 K Next, we prove exact values or upper bounds on the equ...

Let G = (V,E) be an undirected graph, where V is the set of vertices and E is that of edges. An equitable k-coloring of G is a partition of V into k disjoint stable subsets such that the difference on the cardinalities of any two subsets is at most one. Each subset is associated with a color and called a color set. The Equitable Coloring Problem (ECP) consists of finding the minimum value of k ...

Previous studies on handicapping have suggested that in matches between 2 golfers, the better golfer has an advantage. In this paper, we consider medal play between 2 golfers when they are both playing well. The study uses the new slope system for handicapping. In this context we argue that it is actually the weaker golfer who has an advantage. The conclusions are based on both the analysis of ...