Question: Let DIRECTED - HAMILTONIAN - CYCLE be the following problem: given a directed graph D with at least 3 vertices, determine whether D has a

Let DIRECTED-HAMILTONIAN-CYCLE be the following problem: given a directed
graph D with at least 3 vertices, determine whether D has a directed Hamiltonian
cycle, i.e., a cycle which visits every vertex. The goal of this problem is to show that
DIRECTED-HAMILTONIAN-CYCLE is NP-complete.
(a) Show that DIRECTED-HAMILTONIAN-CYCLE is in NP.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

A complete directed network G (V,A) is a directed graph such that for every pair of vertices u, v V , there are arcs u v and v u in A with nonnegative arc lengths d(u, v) and d(v, u),...

Q:

Answer the following questions about a backtracking algorithm for the Travelling Salesman Problem. 3. What would be the states and transitions in a backtracking algorithm for TSP? 4. Given a set of...

Q:

The following questions are about a reduction between the Hamiltonian Cy cle problem (HC) and the Travelling Salesman Problem (TSP). HC is a problem where you and given an unweighted graph, and the...

Q:

Example Assignment Below: Assignment: For each of the eight Recommended Target graph problems (see below), design a real- world problem that can be reduced to the target graph problem. Real-world...

Q:

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

Q:

You have been provided with the description of a programming language, J, intended for scripting applications. Its syntax is similar to a cut-down version of Java in that it consists of function...

Q:

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Q:

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

Q:

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Q:

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Q:

Al-Eman Company purchased a machine on April 1, 2011, at a cash price of (SR 50,000) Related expenditures are for sales taxes (SR 3,000), insurance during shipping (SR 500), and installation and...

Q:

Materials and manufacturing labor variances, standard costs. Dunn, Inc. is a privately held furniture manufacturer. For August 2009, Dunn had the following standards for one of its products, a wicker...

Q:

Toby purchased a twenty - year par value bond with semiannual coupona at a nominal annual rate of 8 % convertible semanmually at a price of 1 , 7 2 2 . 2 5 . The bond can be called at par value 1 . 1...

Q:

Prepare the journal entries to record the following transactions on Cullumber Company's books using a perpetual inventory system. (If no entry is required, select "No Entry"for the account titles and...

Q:

2. What advice will you give her? What do you think are some of the sources of her stress? How will you work with her to develop strategies for reducing her stress?

Q:

1. How do you think and feel about the challenge now, and how did you at the time you faced it?

Q:

4. Fantasy analogy. What is your wildest fantasy about how to solve this problem? How would solving the problem change the future? What is the best possible outcome?