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Q1:3. Prove that any connected graph with minimum degree no less than 3 contains at least three distinct cycles. [5 marks]See Answer
Q2:Ꮖ 4. The following network N has source x and sink y with arc capacities as shown. An initial flow of this network is gi...See Answer
Q3:5. Each game of bridge involves two teams of two partners each. In a bridge club, a game can not be played if any two of...See Answer
Q4:Question 3 (25 marks) This question focuses on Part 3 (selection) and Part 4 (repetition). As inspiration for this quest...See Answer
Q5:Prove that there exists a graph G with 5 nodes such that both G and G (the complement of G) have chromatic number > 3. S...See Answer
Q6:[10 pts] Imagine a country that has n N cities that are linked by highways, where a highway (which can be traversed in e...See Answer
Q7:[10 pts] This problem will use the concept of a graph's degree sequence. This is a list of the degrees of all the vertic...See Answer
Q8:[10 pts] Suppose John's biking environment consists of n ≥ 3 landmarks, which are linked by bike route in a cyclical man...See Answer
Q9:2. Consider a graph G that has k vertices are k-2 connected components, for k >= 4. What is the maximum possible number ...See Answer
Q10:3. Consider the following network of computers: E 3 The numbers labelling each edge indicate the number of Macquariecoin...See Answer
Q11:2. A simple connected graph G has ten vertices of degree 7 and one of degree 6, and no other vertices. (a) [3 marks]. Ho...See Answer
Q12:1. The citizens of the Scandinavian town of Garnsholm are trying to solve a puzzle: is it possible to take a wundertur, ...See Answer
Q13:Ques 2: find the asymptotic upper and lower bound of T(n) = 3T (n-1)? also need to use recursion tree or master theorem ...See Answer
Q14:Ques 1: Find the asymptotic uppler and lower bound of T(n) = 3T(n/2) + n/(log(n)) and T(n) = 3T (n-1). Use recursion tre...See Answer
Q15:We saw in the lectures how to convert a 2-SAT instance into a digraph. Which arcs are created in the digraph from a clau...See Answer
Q16:How many strongly connected components does the graph below have?See Answer
Q17:Q2 6.042 at MIT is often taught using recitations. Suppose it happened that 8 recitations were needed, with two or three...See Answer
Q18:Q1 Because of the incredible popularity of his class Math for Computer Science, TA Mike decides to give up on regular of...See Answer
Q19: 3. (10 pts.) You are in charge of the United States Mint. The money-printing machine has developed a strange bug: it wi...See Answer
Q20: ots.) Consider the following directed graph. 1. What are the sources and sinks of the graph? 2. Give one linearizatio...See Answer

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