Question: Prove that a graph with n nodes and more than n - 1 edges must contain at least one cycle.

Prove that a graph with n nodes and more than n - 1 edges must contain at least one cycle.

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:

Prove that a graph with n nodes and n edges must have at least one circuit.

Q:

Perfect Matching We say that M is a perfect matching if every vertex v V has an incident edge (u, v) M. Note that it is not always possible to find a perfect matching (consider what happens when...

Q:

Prove that any graph with n vertices and at least n + k edges must have at least k + 1 cycles.

Q:

A simple cycle in a graph is a loop that starts from one node and returns to that starting node without visiting any node more than once. The length of a simple cycle is the number of its edges. The...

Q:

Question 3. (1 marks) Let G = (V, E) be an undirected connected graph with n nodes and m edges. In this question you are asked to orient the graph, i.e. pick one direction for each edge: an edge (u....

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

5 . A \ ( k \ ) - coloring of a graph \ ( G = ( V , E ) \ ) is a mapping \ ( f: V \ rightarrow \ { 1 , 2 , \ cdots , k \ } \ ) . That is , the mapping \ ( f \ ) associates with each node in \ ( V \ )...

Q:

1. An undirected graph is said to be connected iff every pair of vertices in the graph are reachable from one another. Prove the following statement: Any connected undirected graph with n nodes has...

Q:

Please provide full solution/explanation A-6-1. A-6-2. A-6-3. A-6-4. {7 marks} For n > 0, the n-triangle (a.k.a. hypertriangle) is the graph whose vertex set consists of all ternary strings (that is,...

Q:

Consider Problem 0.14 (and its solution). Write a Java program that reads in a graph and outputs the clique from pile A and the independent set from pile B. Your program should read from standard...

Q:

What is your opinion of the defense Kraft used in claiming that calcium is an immaterial product attribute?

Q:

A 50.00-mL volume of 0.4987 M HCl was added to a 5.436-g sample of milk of magnesia. This solution was then titrated with 0.2456 M NaOH. If it required 39.42 mL of NaOH to reach the endpoint, what...

Q:

An investor who owns a week - diversified portfolio would consider what to be irrelevant ?

Q:

Seved Help 14 Wisconsin Snowmobile Corp. is considering a switch to level production Cost efficiencies would occur under level production, and aftertax costs would decline by $31,500, but inventory...

Q:

How would redundant storage of values in columns in a Table be eliminated?

Q:

What do Primary Keys, along with Third Normal Form Design in a Database Model, achieve?

Q:

Describe Table Structures in RDMSs.