Question: a. Prove that a forest with c components and n vertices has n - c edges. Assume n c. (Hint: the base case will have

a. Prove that a forest with c components and n vertices has n - c edges. Assume n c. (Hint: the base case will have n = c.)

b. Use the fact proven in the previous problem to show that if a graph has no cycles and has at least n - 1 edges then the graph must be connected.

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:

You$must$attach$this$cover$page$to$the$front$of$your$HW$or$you$will$lose$5$points.$ $ $ APMA$1860$Homework$2$ $ $ First$Name:$____________________________$$$Last$Name:$______________________________$...

Q:

there is no graph the question came like that Question 2: Recall that K, where n 2 is an integer, denotes the complete graph with n vertices. This graph has ) edges, i.e., one edge for each pair of...

Q:

1 CSCI 3 1 1 0 : Assignment 1 ( 6 % of final mark ) posted: May 1 3 th , 2 0 2 4 Instructor: Travis Gagie due: 2 3 : 5 9 May 1 9 th , 2 0 2 4 You are allowed to work in groups of up to 3 . One person...

Q:

1 . Give a diagonalization showing that it is impossible to approximate the Kolmogorov Com - plexity to within a factor of 2 . ( Hint: Modify the diagonalization in the lecture notes. ) 2 . Write a...

Q:

4 ECE 5759 Problem 1. Due: October 25 Closed Convex set in the space of Matrices (10 marks) nn A matrix A R is called a positive semidefinite matrix if xT Ax 0 for every x Rn . Prove that the set of...

Q:

C++ chapter 11. Recursion 11.10 Program: Towers of Hanoi Towers of Hanoi The Towers of Hanoi is a classic problem used to illustrate the power of recursion. The puzzle goes as follows. There are...

Q:

Define a function using recursion in C++ double power(double b, int n) that returns b to the power n. Assume b is nonzero. Hint: return the reciprocal of power(b,-n) when n 0 use the...

Q:

Data gistrun sending inside a pack fills in as conventional allowing subordinate rules to execute on progressive clock cycles. Correspondence between gatherings conventionally causes a surprising...

Q:

search the text name on the Google for book Show written solutions for all of the following problems. Unit 7: Graph Theory Text: Discrete Mathematics: An Open Introduction, 3"I Edition. 4.1...

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:

Consider the following variation of Table 11-1 for the U.S. semiconductor market: a. Fill in the values for W, X, Y, and Z. b. Suppose that before NAFTA the United States had a 20% tariff on imported...

Q:

Listed in the accompanying data table are student evaluation ratings of courses and professors, where a rating of 5 is for "excellent." Assume that each sample is a simple random sample obtained from...

Q:

What is the change in the opportunity cost of increasing the output of capital goods from 20. to

Q:

Please go step by step and create the graph manually, not using excel. 1. Given the following flow rate and BOD concentration data: derived data cumulative volume Table 1: Wastewater Flow Variation...

Q:

How can Federal jobs in the same GS Pay Grade be considered jobs of Comparable Worth?

Q:

What is the Salary Range Midpoint and how does it relate to the Pay Policy Line? For which analytic is it important?

Q:

How wide are Salary Structure Ranges?