Talk:Train track (mathematics)

Ingoing and outgoing

I'm not sure what's going on with the latest edits, in particular the comments in the edit box about ingoing and outgoing, but I thought I should clear up the confusion. The usual thing to do is to stick with one convention: at each switch, either have one ingoing and two outgoing or have two ingoing and one outgoing. This has nothing to do with directed graphs or any kind of orientation for the train track. It is merely a linguistic device used to indicate the local picture at a switch, i.e. which way the cusp is pointing (c.f. the comments about C^1 structure).

Thus we should stick with one convention, which currently is to have one ingoing branch and two outgoing at each switch. --C S 04:55, Dec 20, 2004 (UTC)

Confluent drawing

I don't want to add it myself because it's too much my own work, but whoever's editing this page might want to take a look at confluent drawing, a technique in Graph drawing closely related to train tracks. —David Eppstein 01:05, 13 September 2006 (UTC)[reply]

Definition

The definition seems wrong to me. There's no geometry condition (The double of the connected components must have negative Euler characteristic). The third condition doesn't ensure this and the wording may be bad also, If you want a trivalent track as the definition then locally three curves meet, the curves don't have to come from different edges. Avaldivi (talk) 18:44, 19 April 2010 (UTC)[reply]

I also wonder about the definition.

Must a train track be connected?
Can an arc of a train track just stop, with no switch?
Can an arc of a train track meander about forever, without any end?

The article's definition implies no, yes, and yes. Maproom (talk) 12:48, 29 April 2014 (UTC)[reply]