jack

Question 1

You have a graph on an even number P people where each node has E=3 edges connected to it. You colour in one edge. Then you colour in another edge such that each person has at most one coloured edge, aka not touching a previous coloured edge (without planning ahead). You keep doing this as long as you can.

I think for some graphs (e.g. 4 people, or 6 people each connected to the adjacent people and the opposite person) you are guaranteed to be able to colour P/2 edges so that each person touches exactly one coloured edge, whatever your early choices were. Whereas for other graphs (e.g. the corners of a triangular prism?) you can end up in a "dead end" where you've coloured two edges and then the two people left over with no coloured edge have no edge between them to colour.

Is there a description of which graphs guarantee and which don't? What about if E=2 (probably usually not guaranteed?). Or E=4?

Question 2

You have a graph with even P nodes each with E=3 edges. There are A=3 acts. In the first, you colour P/2 non-touching edges. In the second you colour P/2 non-touching edges, not colouring edges that were coloured in act 1 (without planning ahead to act 3). In the third act, you also try to colour P/2 non-touching edges that weren't coloured in acts 1 or 2. Are there graphs where if you colour the edges one at a time you're guaranteed to fill in all the edges without discovering you need to backtrack?

What about for different values of E and A? If E is greater than A? If E is ALL the possible edges then it's always possible, but for values less than that?

Question 3

You have a graph with even P nodes each with E=3 edges. There are A=3 acts. In the first, you colour P/2 non-touching edges with +1, 0 or -1. In the second you colour P/2 non-touching edges, not colouring edges that were coloured in act 1, with +1, 0 or -1 (without planning ahead to act 3). In the third act, you also try to colour P/2 non-touching edges that weren't coloured in acts 1 or 2, also with +1, 0 or -1, but try to ensure that three values each node touches sum to 0. Are there graphs that guarantee that's possible in act 3, regardless of what you did in acts 1 and 2?

What if you had E=4 and coloured +1 or -1?

I'm happy: I think I've got the hang of it, and the system -- while I don't know how it compares to other LARP systems -- seems pretty good in absolute, and hitting people with swords is fun -- fencing actually comes in handy, woop!

Though I feel kind of bad that everything I did went wrong. Which isn't a big deal, it's only LARP, and isn't anyone's fault including mine, but all the time I seem to have conversations like:

Someone else: What are you doing here?
My character: [Paraphrases ref's brief, typically "You're a guard patrolling here for blah."]
Someone else: Why the hell are you doing that? Who sent you?
My character: Uh, [adlib]
Someone else: Gah! All guardsmen seem to be idiots.
Me: What am I supposed to do? If I adlib, it's false in character. If I go and ask a ref every question I think my NPC would know the answer to, I'll hold the game up 5 minutes a time. I read all the rules, and was given a one-line description with no motivation, but can't know what's normal in this situation, and taking cues from people who've played before just makes it worse. I'm sorry!

But it was overall good and I will come back next time and do it right. And hopefully develop a character this week for the interactive. And fight chessypig with rubber swords any time the opportunity presents itself :)