Last wins - DPChallenge Forums

01/13/2011 02:52:53 PM · #4701

*crumple crumple rip shred chomp chomp*

01/13/2011 06:08:11 PM · #4702

so...I guess I'm still winning...

Canon EF 24-70mm f/2.8L USM

01/13/2011 07:25:03 PM · #4703

guess again.

goinskiing

Canon EOS-6D

01/13/2011 07:26:42 PM · #4704

We all know I'll win, nice try Art.

01/13/2011 07:27:11 PM · #4705

what are you two talking about!!! I WIN...no need to respond

01/13/2011 07:30:20 PM · #4706

If I ever waited for a "need" to respond, I would disappear from this site completely. :P

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

01/13/2011 07:56:22 PM · #4707

You do have a point Ken...

Apple iPhone 5

01/13/2011 07:59:20 PM · #4708

Must....resist....

The needs of the many outweigh the needs of the few. Or the one.

Canon EF 24-70mm f/2.8L II

01/14/2011 01:56:46 AM · #4709

resistance is futile. bow to your superior "Last wins" competitor.

bergiekat

Canon EOS-5D Mark IV

01/14/2011 02:30:01 AM · #4710

this is not some silly square dance...there will be no bowing!

01/14/2011 02:43:02 AM · #4711

Damn. Then I better change my shoes.

TrollMan

Fujifilm X-T4

Fujifilm XF 35mm f/1.4

01/14/2011 02:49:54 AM · #4712

How about bowling? I'm sure Ken wouldn't mind being a pin.

01/14/2011 02:57:28 AM · #4713

Alllllrighty. Now I have to go change my shoes once again.

bvy

Sigma DP1x

01/14/2011 08:22:21 AM · #4714

Good morning. A planar graph has a vertex of degree less than or equal to five.

Proof: The result is obvious for planar graphs with six or fewer vertices since the maximum degree of any vertex is five.

Let G(p, q) be a planar graph with p >= 7, and suppose G has no vertices of degree less than or equal to five. Then every vertex of G has degree six or greater. The sum of the degrees of the vertices is 2q which must be greater than or equal to 6p, since each of p vertices has degree six or greater. So 2q >= 6p or q >= 3p. However, a corollary of Eulerâ��s formula (p â�� q + r = 2 where r is the number of regions of a planar graph) states that q <= 3p â�� 6. Combining these results, we get 3p <= q <= 3p â�� 6, or 3p <= 3p â�� 6, which is a contradiction. Hence, G must have some vertex of degree less than or equal to five.

We will use this result later.

Sony DT 18-70mm f/3.5-5.6 Aspherical ED Zoom Lens for Sony Alpha

01/14/2011 09:04:52 AM · #4715

oh, good grief Brian...it's just way to early for this....I will have to say "I win" again

the99

Sony DSLR-A100

01/14/2011 01:00:57 PM · #4716

I REALLY LOVE bowling!

01/14/2011 01:35:50 PM · #4717

Well I do too...maybe we should all meet there...I win

01/14/2011 05:12:46 PM · #4718

Win again, I do.

01/14/2011 06:35:52 PM · #4719

yes...I do win again...thanks Art...

01/14/2011 06:45:21 PM · #4720

(>.<)

01/14/2011 07:02:57 PM · #4721

and again....

01/14/2011 07:07:40 PM · #4722

Tennis, anyone?

01/14/2011 07:08:23 PM · #4723

stomps foot!!!! I WIN...NO NEED TO RESPOND....HUMF

01/14/2011 07:10:46 PM · #4724