Isn't the simplest solution that everybody shakes hand with Byron? Everybody but Byron has one handshake and Byron has n-1, with n the number of people
Depending on your definition of simpler, everyone could just pair off and shake exactly one hand.
What a Math Party Game Tells Us About Graph Theory
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Re: What a Math Party Game Tells Us About Graph Theory
#12Title is backwards. graph theory tells us about the party game.
Re: What a Math Party Game Tells Us About Graph Theory
#13Isn't the simplest solution that everybody shakes hand with Byron? Everybody but Byron has one handshake and Byron has n-1, with n the number of people
It's the simplest option when n is even (which it is in this case), but fails when n is odd.
Re: What a Math Party Game Tells Us About Graph Theory
#14Isn't the simplest solution that everybody shakes hand with Byron? Everybody but Byron has one handshake and Byron has n-1, with n the number of people
The article about how this problem is trivial for N even but impossible for N odd.
Re: What a Math Party Game Tells Us About Graph Theory
#15The solution, when dealing with an odd number of folks, is to do a 'three-way' handshake. Some times you have to think outside the box.
That's 2 per person, or an impossible shake, since a hand is half a pair.
Re: What a Math Party Game Tells Us About Graph Theory
#16While the title is entertaining this doesn’t seem to be a very good candidate for a game at a party.
Re: What a Math Party Game Tells Us About Graph Theory
#17Isn't the simplest solution that everybody shakes hand with Byron? Everybody but Byron has one handshake and Byron has n-1, with n the number of people
The article about how this problem is trivial for N even but impossible for N odd.
The article is talking about the biggest odd subgraph within the even subgraph solution.
I think the problem with the suggestion is that the solution to the even subgraph may not be under your control? Not sure.
Re: What a Math Party Game Tells Us About Graph Theory
#18The solution, when dealing with an odd number of folks, is to do a 'three-way' handshake. Some times you have to think outside the box.
That's 2 per person, or an impossible shake, since a hand is half a pair.
Nah, its half a handshake with each person, so only one total handshake per person :)
Re: What a Math Party Game Tells Us About Graph Theory
#19Earlier quoted context omitted.
The goal of the game is to end with everyone having an odd number of handshakes. I'll also add that his comment about winning/losing is a bit off as well. This isn't a competitive game, it's a cooperative one. Everyone needs to shake an odd number of hands. The game is won, when everyone in the room has shaken an odd number of hands. It's more a puzzle than a game. There may be additional rules on if disconnected sub…
Cooperative games still allow a distinction between winning and losing moves. A winning move is one where the resulting subgame still has a solution. A losing move is one where the resulting subgame has no solution. In this game, looking only at the parities, all moves are reversible, so every move preserves the property of having a solution. For an even number of nodes, all moves in all positions are winning. And fo…
Yes, but before that person had an even number of handshakes, so shaking their hand gets them to odd. But at the expense of putting him at even. At worst, it's a neutral move.
And like I said, it really depends on the other rules which are never explicitly stated.
But I have a sneaking suspicion that discussing the game is arguing the metaphor.
The game is just there to help us get to the realization that graphs with an even number of vertices can have an odd number of edges, but a graph with an odd number of vertices can't have an odd number of edges.
Re: What a Math Party Game Tells Us About Graph Theory
#20Earlier quoted context omitted.
Cooperative games still allow a distinction between winning and losing moves. A winning move is one where the resulting subgame still has a solution. A losing move is one where the resulting subgame has no solution. In this game, looking only at the parities, all moves are reversible, so every move preserves the property of having a solution. For an even number of nodes, all moves in all positions are winning. And fo…
Yes, but before that person had an even number of handshakes, so shaking their hand gets them to odd. But at the expense of putting him at even. At worst, it's a neutral move. And like I said, it really depends on the other rules which are never explicitly stated. But I have a sneaking suspicion that discussing the game is arguing the metaphor. The game is just there to help us get to the realization that graphs with…
> a graph with an odd number of vertices can't have an odd number of edges.
A 3 node graph can have 1 edge. The article is about a different notion of oddness, namely that all nodes have an odd degree.