Splitting finite antichains in the homomorphism order

Foniok, J and Nesetril, J (2008) Splitting finite antichains in the homomorphism order. In: ROGICS'08 Relations, Orders and Graphs: Interaction with Computer Science, 12-17 May 2008, Tunisia.

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Abstract

A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.