Minimum vs Minimal vertex covers

Posted by panicked on Stack Overflow See other posts from Stack Overflow or by panicked
Published on 2010-06-15T04:59:44Z Indexed on 2010/06/15 5:02 UTC
Read the original article Hit count: 292

Filed under:

minimum

|

vertex

|

minimal

|

cover

I am studying for an exam and one of the sample questions is as follows:

Vertex cover: a vertex cover in a graph is a set of vertices such that each edge has at least one of its two end points in this set.

Minimum vertex cover: a MINIMUM vertex cover in a graph is a vertex cover that has the smallest number of vertices among all possible vertex covers.

Minimal vertex cover a MINIMAL vertex cover in a graph is a vertex cover that does not contain another vertex cover (deleting any vertex from the set would create a set of vertices that is not a vertex cover)

Question: A minimal vertex cover isn't always a minimum vertex cover. Demonstrate this with a simple example.

Can anyone get their head around this? I am failing to see the distinction between the two. More importantly, I'm having a hard time visualizing it.

I seriously hope he's not gonna ask odd questions like this one on the exam!

© Stack Overflow or respective owner

Related posts about minimum

Minimum confidence and minimum support for Apriori

as seen on Stack Overflow - Search for 'Stack Overflow'
What are appropriate values for minimum confidence and minimum support values for the Apriori algorithm? How could you tweak them? Are they fixed values, or do they change during the running of the algorithm? If you have used this algorithm before, what values did you use? >>> More
Minimum number of disks to implement RAID6

as seen on Server Fault - Search for 'Server Fault'
Hi All, RAID6 is intended to provide fault tolerance in the event 2 disks fail. What is the minimum number of disks required to implement RAID6? thanks >>> More
SVM Classification - minimum number of input sets for each class

as seen on Stack Overflow - Search for 'Stack Overflow'
Im trying to build an app to detect images which are advertisements from the webpages. Once I detect those Ill not be allowing those to be displayed on the client side. From the help that I got here in stackoverflow, I thought SVM is the best approach to my aim. So, I have coded SVM and an SMO myself… >>> More
How to find minimum of nonlinear, multivariate function using Newton's method (code not linear algeb

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm trying to do some parameter estimation and want to choose parameter estimates that minimize the square error in a predicted equation over about 30 variables. If the equation were linear, I would just compute the 30 partial derivatives, set them all to zero, and use a linear-equation solver. … >>> More
Convert methods from Java-actionscript to ObjectiveC

as seen on Stack Overflow - Search for 'Stack Overflow'
Hi I'm tring to convert the following 3 methods from java-actionscript to Objective C. Part of my confusion I think is not knowing what Number types, primitives I should be using. ie in actionscript you have only Number, int, and uint. These are the 3 functions I am trying to convert public function… >>> More

Related posts about vertex

GLSL vertex shaders with movements vs vertex off the screen

as seen on Game Development - Search for 'Game Development'
If i have a vertex shader that manage some movements and variations about the position of some vertex in my OpenGL context, OpenGL is smart enough to just run this shader on only the vertex visible on the screen? This part of the OpenGL programmable pipeline is not clear to me because all the sources… >>> More
how can I specify interleaved vertex attributes and vertex indices

as seen on Game Development - Search for 'Game Development'
I'm writing a generic ShaderProgram class that compiles a set of Shader objects, passes args to the shader (like vertex position, vertex normal, tex coords etc), then links the shader components into a shader program, for use with glDrawArrays. My vertex data already exists in a VertexBufferObject… >>> More
change the color of a vertex in a vertex shader

as seen on Stack Overflow - Search for 'Stack Overflow'
Is it possible to set the color of a single vertex using a GLSL vertex shader program, in the same way that gl_Position changes the position of a vertex ? >>> More
set the color of a vertex using a GLSL vertex shader

as seen on Stack Overflow - Search for 'Stack Overflow'
Is it possible to set the color of a single vertex (not a face) using a GLSL vertex shader program (using GL_ARB_shading_language_100 extension) ? >>> More
AndEngine Physics Editor loading level

as seen on Stack Overflow - Search for 'Stack Overflow'
I have created a .pes file using PhysicsEditor and imported as xml and have added to my project. When I parsed it and created bodies, it is showing strange behavior. The mapping of bodies that I created in PhysicsEditor is totally different what I see in my application means the shapes I draw in PhysicsEditor… >>> More