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Showing posts 23151 - 23175 of 30665, (reverse)
AuthorThread
 10/23/2013 10:16:59 PM · #23151
Just returned from the K-man islands.

I win, tax-free!
 10/24/2013 12:09:15 AM · #23152
Knock Knock

Who's There?

The IRS.

The IRS who?

The IRS coming to arrest Art for tax fraud.

Sure, come on in, Art's in the kitchen.

Spork wins
 10/24/2013 12:35:55 AM · #23153
Catch me if you can.
 10/24/2013 01:52:57 AM · #23154
yessss ...if you can
 10/24/2013 02:45:04 AM · #23155
Really, it's not that hard, I'm pretty slow.
 10/24/2013 08:53:25 AM · #23156
That sounds like my great-uncle. Back during prohibition, he used to run moonshine and was known for always having a fast car and his ability to lose the cops. He also developed a strong dislike for law enforcement that stayed with him til the end. In the 1970's, he was driving down a road in town and a cop noticed that his tail light was out and thought he pull him over to let him know and probably write him a warning. I guess he figured that a little old man would just pull over. My great uncle, upon seeing the flashing red and blue lights did not slow down and pull over, noooo he did not. Instead, he hit the gas and headed out of town, thinking that if he could make it out onto the maze of unpaved country roads, he could lose this clown. Unfortunately, his driving skills were what they had been 50 years prior and he went off the road, through a farmer's fence and got the car stuck. Instead of giving up, he gets out of the car and heads towards the woods on foot...with his cane. The cop later said that when the he saw my uncle heading across the field at a snail's pace, he was laughing so hard that he almost couldn't give chase. My uncle must have thought he still had a chance to get away since he took a swipe at the cop with his cane. Needless to say, he was finally apprehended and brought home to my aunt in the back of the cop car.

Spork wins
 10/24/2013 05:20:53 PM · #23157
Great story, Spork. That was the 70's. Today, he would have been gunned down before he got out of his car.

I win.
 10/24/2013 10:37:52 PM · #23158
Yeah, no kidding. He'd have been labeled a terrorist first though.

Spork runs moonshine and wins.
10/24/2013 10:42:15 PM · #23159
Spork has now been placed on the Federal No-Win List.
 10/25/2013 01:31:05 PM · #23160
Spork wins despite the Feds
 10/25/2013 03:27:11 PM · #23161
I feel like Bastian Bux.
 10/25/2013 04:11:01 PM · #23162
I feel like I should google that, but I am too lazy.
 10/25/2013 04:28:45 PM · #23163
I'm too lazy to even feel like googling it.
 10/25/2013 05:07:58 PM · #23164
I googled. I win. Not because I googled. Just because I win.
 10/25/2013 06:27:19 PM · #23165
10/25/2013 09:04:35 PM · #23166
Nope!
 10/25/2013 09:08:51 PM · #23167
Not even close!

How old are you anyway? And do you have any major health problems? I am going to my bookie and laying odds that I can outlast you...www.artwins.com will have to post a major retraction after I win. And you won't even be here to see it. Consistent my rump! Lucky if you ask me.

;)

Message edited by author 2013-10-25 23:11:42.
 10/26/2013 12:20:43 AM · #23168
ok I have been away for awhile....I still win
 10/26/2013 11:49:40 AM · #23169
No, while you were away, everyone agreed that Spork wins.
 10/26/2013 01:51:18 PM · #23170
I agreed to no such thing. Now that cowboy is back, I win.
 10/26/2013 08:54:43 PM · #23171
You did too.

Spork wins.
 10/26/2013 09:32:18 PM · #23172
Did not.

I wins.
 10/27/2013 12:38:12 AM · #23173
Liar, Liar pants on fire.

Spork wins.

10/28/2013 08:05:38 AM · #23174
Originally posted by bvy:
Recall that a graph G is k-degenerate if every induced subgraph H of G has d(H) <= k. A graph has degeneracy k if it is k-degenerate but not (k-1)-degenerate. Trees and forests (graphs containing no cycles) have degeneracy 1. All planar graphs are 5-degenerate, although a planar graph can have degeneracy less than 5 (e.g. trees are planar).

A k-degenerate graph G is maximal k-degenerate if for any two non-adjacent vertices u, v of G, the graph G+uv is not k-degenerate.

I would like to prove that if G is a maximal k-degenerate graph of order n >= k+1, then d(G) = k.


Good morning. Sorry for the delay. Suppose G is a maximal k-degenerate graph of order n >= k+1 and that d(G) < k. Let u be a vertex of G having minimal degree, d(G). Let H = G - u be the induced subgraph of G containing all vertices but u. Then there must be some vertex v of H not adjacent to u, for H has order >= k, but u is adjacent to, at most, k-1 vertices. We add the edge uv to G and observer that the degree of u is now, at most, k, and any induced subgraph of G still has d(G) <= k. Hence, G+uv is k-degenerate, which is a contradiction, since G is supposed to be maximal k-degenerate. Therefore d(G) = k.
10/28/2013 09:04:33 AM · #23175
Originally posted by bvy:
Originally posted by bvy:
Recall that a graph G is k-degenerate if every induced subgraph H of G has d(H) <= k. A graph has degeneracy k if it is k-degenerate but not (k-1)-degenerate. Trees and forests (graphs containing no cycles) have degeneracy 1. All planar graphs are 5-degenerate, although a planar graph can have degeneracy less than 5 (e.g. trees are planar).

A k-degenerate graph G is maximal k-degenerate if for any two non-adjacent vertices u, v of G, the graph G+uv is not k-degenerate.

I would like to prove that if G is a maximal k-degenerate graph of order n >= k+1, then d(G) = k.


Good morning. Sorry for the delay. Suppose G is a maximal k-degenerate graph of order n >= k+1 and that d(G) < k. Let u be a vertex of G having minimal degree, d(G). Let H = G - u be the induced subgraph of G containing all vertices but u. Then there must be some vertex v of H not adjacent to u, for H has order >= k, but u is adjacent to, at most, k-1 vertices. We add the edge uv to G and observer that the degree of u is now, at most, k, and any induced subgraph of G still has d(G) <= k. Hence, G+uv is k-degenerate, which is a contradiction, since G is supposed to be maximal k-degenerate. Therefore d(G) = k.


Spork thinks YOU are the degenerate and that you should quit picking on others.

Spork wins
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