Extendability, Dimensions, and Diagrams of Cyclic Orders
Peter Alles, Jaroslav Nešetřil, Svatopluck Poljak · SIAM Journal on Discrete Mathematics · 1991
Several classes of cyclic orders arising from geometrical, algebraical, and combinatorial structures are introduced, and their extendability to total cyclic orders is studied. By analogy to Dushnik–Miller dimension for partial orders we define, for circular orders, intersection and product dimension that may differ up to a factor of two. A class of cyclic orders that allow a graphic representation similar to Hasse diagrams is also studied.