Last wins - DPChallenge Forums

02/10/2015 10:16:05 AM · #26752

outta the way

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

02/10/2015 10:48:40 AM · #26753

I still not am at the losing end big so.

But I am in the pub.

Win everyway

RyanW

Nikon D7000

02/10/2015 11:15:54 AM · #26754

but you're at the end of a thread of losing posts, I'd say that puts you at the losing end.

Message edited by author 2015-02-10 11:16:13.

Spork99

OM System OM-1

Canon EF 100mm f/2.8 USM Macro

02/10/2015 12:18:50 PM · #26755

Spork is the be all, end all of winning.

Spork wins.

skewsme

Canon EOS-6D

Canon EF 200mm f/2.8 L II USM Lens

02/10/2015 01:01:26 PM · #26756

spork is be-alled up in the corner, crying about the end-all of his win.

Spork99

OM System OM-1

Canon EF 100mm f/2.8 USM Macro

02/10/2015 01:10:30 PM · #26757

Oh thank you dear Ms. Skewers.

Spork is making shish kebabs.

Spork wins

02/10/2015 05:24:03 PM · #26758

I love your new skirt.

02/11/2015 11:24:12 AM · #26759

WAAAAASSSSSSUUUUPPPPP!!!!!!!!!!!!!!!!!!

02/11/2015 11:58:20 AM · #26760

For example, we can show that all regular graphs of odd order are of class 2. If G is r-regular with order n. then the size of G is rn/2. D(G) = r, and n/2 > floor(n/2) since n is odd. Hence m = r (n/2) > r floor(n/2).

This is a simple application of the overfull corollary.

02/11/2015 12:12:26 PM · #26761

How much wood, could a woodchuck chuck, if a woodchuck could chuck wood??

02/11/2015 12:22:27 PM · #26762

It really suits you.

02/11/2015 02:12:01 PM · #26763

Originally posted by cowboy221977:

How much wood, could a woodchuck chuck, if a woodchuck could chuck wood??

FAIL!

How much wood WOULD a woodchuck chuck if a woodchuck COULD chuck wood?

In other words, the metrics are capability vs desire; plug those into one of them high-falutin' graphs, boys, and derive us an answer...

Message edited by author 2015-02-11 14:12:23.

02/11/2015 03:17:06 PM · #26764

He'd chuck 361.9237001 cubic centrimeters of wood per day, which is the wood that a woodchuck COULD chuck, if a woodchuck could chuck wood.

Message edited by author 2015-02-11 15:21:09.

02/11/2015 04:14:08 PM · #26765

Originally posted by cowboy221977:

He'd chuck 361.9237001 cubic centrimeters of wood per day, which is the wood that a woodchuck COULD chuck, if a woodchuck could chuck wood.

I'll meet you halfway: make it how much wood he COULD chuck if he felt the desire to (WOULD chuck)... Your version is jus unacceptable to analytic Bear, capisce?

Pentax DA 18-135mm F3.5-5.6ED AL [IF] WR DC

02/11/2015 05:24:56 PM · #26766

It's also relatively straightforward to show that we can remove a certain number of edges from a regular graph of odd order which is class 2, and have it remain class 2. Specifically, we can remove 1/2 (D(G) - 1) edges.

Let G be an r-regular graph of odd order n, as described above, and observe that D(G) = r and (n-1)/2 is an integer. Since G is r-regular, the size of G is m = rn/2. Now let's remove 1/2 (D(G) - 1) edges to arrive at a new graph G'. The size of G' is:

m' = rn/2 - 1/2(r - 1) = (rn -r + 1)/2 = r (n - 1)/2 + 1/2 > r (n-1)/2.

Observe that our last term, r (n-1)/2 = r floor(n/2), and so the overfull corollary holds once again, and our new graph G' is also of class 2.

tnun

Ricoh GR III

02/11/2015 10:29:41 PM · #26767

overfull corollas do NOT hold up, not once, not again. 2nd class is 2nd class.

02/11/2015 11:58:41 PM · #26768

Originally posted by bvy:

Observe that our last term, r (n-1)/2 = r floor(n/2), and so the overfull corollary holds once again, and our new graph G' is also of class 2.

Brian, I have a few Valiums around here somewhere if that would help?

02/12/2015 09:22:24 AM · #26769

Valium? No! We're making good progress. A stimulant is what's called for.

"A mathematician is a device for turning coffee into theorems." -Paul Erdos

Canon EF 100mm f/2.8 USM Macro

02/12/2015 09:48:01 AM · #26770

And I think the fit. / color is all yours.

Still I win

Spork99

OM System OM-1

02/12/2015 07:58:20 PM · #26771

I hope you got a receipt with thatâ�¦

Spork wins.

Canon EF-S 18-200mm f/3.5-5.6 IS

02/12/2015 08:51:01 PM · #26772

So, again, the preceding doesn't preclude r-regular graphs of even order from being class 2. The most famous example of this is probably the Petersen graph. The Petersen graph is 3-regular and has order 10, but cannot be edge colored with fewer than three colors. I'd like to provide a constructive proof this.

CEJ

Canon EOS-40D

02/12/2015 09:03:41 PM · #26773

Well, by all means, provide away! This thread DOES NOT CONTINUE until you provide the proof - irrefutable of course!

Message edited by author 2015-02-12 21:05:25.

02/12/2015 11:17:53 PM · #26774

THE Peterson graph? Isn't that the "God graph"? The one that has to be taken on faith? This thread is OVER! By coincidence, I win. Shall I lock it?