Last wins - DPChallenge Forums

Nikon AF-S DX NIKKOR 18-200mm f/3.5-5.6G ED VR II

01/19/2011 10:12:35 AM · #4801

Pffft! We'll just knock out walls until we have one room that's big enough.

bvy

Sigma DP1x

01/19/2011 10:18:25 AM · #4802

Originally posted by JH:

Originally posted by bvy:
I define G2 as the connected component subgraph of G - v having, as shown, all blue and green vertices conneceted to v2. The v1-v3 path is shown in red and yellow; it circumscribes G2. G2 cannot contain v4 -- to make the connection, there would have to be a v2-v4 path in G2, and the only way to get to v4 from v2 is to cross the v1-v3 path. (All casually stated.)

Ahhhh... but what about these itty-bitty little corners, the bits that are just touching each other?.. You might not think it, but they are. Like two lovers brushing lips as they gently kiss... these two colours are touching.

And don't start telling me there's a line between them. Yeah, now I think about it - What about your lines? - You've got lines in your graphs, black lines. And black is a colour, kind of. So that's 6 colours, and all the colours are touching black.

Lovers brushing lips? You've made a mockery of my proof, and that's really not fair to the regulars here who hold graph theory near and dear to their hearts.

More to the point, you're as screwy as I am.

Ja-9

Nikon D750

01/19/2011 10:26:31 AM · #4803

I'm thinking theres not near enough room anywhere on this planet for all of you guys to make a "man cave"...it would be way, way, way to crowded....

01/19/2011 02:01:25 PM · #4804

*epiphany*

*whistles*...oh boys, there is going to be a new man cave...out back!!!

Grab your shovels and make one! In the mean time, there is an interior decorator coming over and I've offered up all of your crap to Goodwill!

01/19/2011 02:26:32 PM · #4805

* TrollMan chains himself to the beer keg...and the mechanical bull * "Over my body mrs!"

Nikon AF-S DX Zoom-Nikkor 18-55mm f/3.5-5.6 ED

01/19/2011 02:34:37 PM · #4806

Originally posted by bvy:

You've made a mockery of my proof

JH made a mockery and I made a dartboard, which demonstrates the versatility of your graph.

* also chains himself to the keg (but not to the bull) *

We're probably gonna need this.

Apple iPhone 5

01/19/2011 06:20:01 PM · #4807

Originally posted by Art Roflmao:

What's the scoring system?

01/19/2011 06:34:10 PM · #4808

Originally posted by JH:

What's the scoring system?

Ask

bvy.

bvy

Sigma DP1x

01/19/2011 06:55:17 PM · #4809

Well, I, uh... Is that my graph in a urinal?

01/19/2011 08:06:00 PM · #4810

Originally posted by bvy:

Well, I, uh... Is that my graph in a urinal?

What else would we use it for (other than a dartboard)?

I am winning (at the Urinal Target Game AND this thread).

bvy

Sigma DP1x

01/19/2011 08:16:02 PM · #4811

I've spent the last several days trying to find a clever proof for the following problem: Show that any planar graph of order two or greater has at least two vertices of degree less than or equal to five.

A few things about this. We've already shown that a planar graph has at least one vertex of degree less than or equal to five. However that proof was by contradiction: suppose that every vertex has degree greater than or equal to six.

I'm convinced that the proof must be by induction -- similar to the approach taken on the Five Color Theorem. Start with the planar graph on two vertices (isomorphic to K2). It has two vertices each of degree one and our base case is established.

Now suppose our planar graph has k vertices. We can remove a vertex and have a graph of order k - 1 for which the hypothesis holds. But which one do we remove? We can pick one arbitrarily, call it v, and if v is not incident with whatever vertices in G - v happen to be of degree less than or equal to five, than we're okay. But what if it is connected to one or both of these vertices?

I'm still thinking on this, but I will be curious to hear if the group has any feedback.

01/19/2011 08:28:00 PM · #4812

Am I gonna need to get another urinal?

01/20/2011 01:08:46 AM · #4813

Originally posted by Art Roflmao:

Am I gonna need to get another urinal?

No, but you're going to have to get outta the way when the painters get here...and those shall be your color choices! :P

01/20/2011 03:26:33 AM · #4814

Don't forget, TrollMan and I are still chained to the keg and the bull. ...and I just passed out.

01/20/2011 03:35:10 AM · #4815

I new Are was chained to the keg, but he refrained from the bull...
...you on the other hand....bull, good description, muahahaha! And I must say, that photograph of you back in '82 will find a place of honor.
Now, rub my feet!

01/20/2011 03:40:53 AM · #4816

Originally posted by bergiekat:

Now, rub my feet!

Ok, but first soak them in this foot massaging oil...

01/20/2011 03:45:09 AM · #4817

Oooooh, the good callus remover stuff! ;P

01/20/2011 04:24:47 AM · #4818

oops, let me get my other pedicure tools...

01/20/2011 04:29:04 AM · #4819

and we can do your eyebrow while we're at it! :p
*** runs ****

01/20/2011 05:24:07 AM · #4820

Whatchyoutalkin 'bout, Kat??

01/20/2011 05:39:06 AM · #4821

Don't let the girls remove your unibrow Art, or you might look like this... OUCH!

01/20/2011 05:58:57 AM · #4822

*faints from the sight of blood*

01/20/2011 06:02:24 AM · #4823

Riiight. And I faint at the sight of booze...and woman riding on mechanical bulls. "Stay away from our mechanical bull girls!" :P

01/20/2011 06:08:20 AM · #4824

Dayum!