1ECONOMICS AND QUANTITATIVE ANALYSIS (ONLINE)CALCULATIONS & SHORT WRITTEN RESPONSESINSTRUCTIONSUndertake the necessary calculations and prepare short written responses for the followingfour questions. Answers for each question must not exceed 250 words.Question 1 (5 marks)Special Agent Fox Mulder has a budget of $180. He spends it on conspiracy theorymagazines (good X) and UFO videos (good Y). Each […]

1811132 Group Project Assignment Hints1. Discuss among your team of each of your skills. You may use a table to record theskills. These are more like the soft skills for executing the following tasks likedevelop project plan; resources planning, drawings and writing specifications;produce cost plan; safety statement etc. These are mainly the project planningskills on

Use Dilworth’s theorem to derive the marriage theorem. We remark that our proof of Theorem 7.5.2 is also interesting from an algorithmic point of view, since it allows to calculate the Dilworth number of G by determining a maximal matching in the bipartite graph H, because of Δ = n − α_(H). Thus Theorem 7.5.2

Suppose we are given a supply and demand problem where the functions c, a, and d are integral. If there exists a feasible flow, is there an integral feasible flow as well? Show that a k-connected graph on n vertices contains at least _kn/2_ edges. (Note that this bound is tight; see [Har62].)

Let G = (V,E) be a k-connected graph, T a k-subset of V , and s ∈ V T. Show that there exists a set of k paths with start vertex s and end vertex in T for which no two of these paths share a vertex other than s. Show that Theorem 8.1.4 is

Prove that in fact ch() = 3. Hint: Use a case distinction according to whether or not two color lists for vertices in the same part of the bipartition have a color in common. By a result of [ErRT80], there are bipartite graphs with an arbitrarily large choosability; thus k-choosability can indeed be a much

Let G be the digraph given in Figure 10.2 with capacity constraints b and c. We require a feasible circulation on G. By Theorem 10.2.1, we have to determine a maximal flow for the network N shown in Figure 10.3. In general, we would use one of the algorithms of Chapter 6 for such a

Let G be a mixed multi graph. Find necessary and sufficient conditions for the existence of an Euler tour in G; cf. Exercise 10.1.6. Let N = (G, b, c, s, t) be a flow network with a nonnegative lower capacity b. Describe a technique for determining a minimal feasible flow on N (that is,

Let G be a connected digraph with capacity constraints b and c, where b(e) is always positive and c(e) = ∞ for all edges e. Show that G has a feasible circulation if and only if it is strongly connected. Moreover, give a criterion for the existence of a feasible flow if we also specify

Let G be a 3-regular graph without bridges. Show that G has a perfect matching [Pet91]. Does this also hold for 3-regular graphs containing bridges? Does a 3-regular graph without bridges necessarily have a 1-factorization? Let G = (V,E) be a digraph having n vertices, m edges, and p connected components. Let M be the