Timeline for Does a notion of convex graph make sense?
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| May 5, 2016 at 15:05 | comment | added | Anurag | This exact definition is also used in the theory of near polygons: en.wikipedia.org/wiki/Near_polygon. One of the most basic/important structural result for near polygons is about existence of "quads", which are basically convex subsets isomorphic to generalized quadrangles: en.wikipedia.org/wiki/Generalized_quadrangle, roughly under the condition that every two points at distance 2 from each other have more than one common neighbours. | |
| Sep 10, 2013 at 13:13 | comment | added | Sergiy Kozerenko | To be precise there exist much more types of convexity of vertex sets in graphs. One can talk about geodesic convexity, monophonic convexity, "all-path" convexity, "induced-path" convexity and generally about convexities induced by different path transit functions. | |
| Nov 3, 2011 at 17:52 | comment | added | Valerio Capraro | This is a definition that makes sense also for subsets, since every graph is convex in itself according to this definition. I am looking for some property of the graph. Anyway, thanks for pointing out that there is a standard definition of a convex set in a graph. | |
| Nov 3, 2011 at 15:01 | history | answered | David Eppstein | CC BY-SA 3.0 |