Publication at Faculty of Mathematics and Physics |
2011
Abstract
Relational structure is homomorphism-homogeneous if every local homomorphism between finite induced substructures can be extended to endomorphism. The clas- sification of homomorphism-homogeneous relational structures is still a challenging problem even for a finite case.
In this work finite homomorphism-homogeneous binary relational structures having two relations that are both symmetric and ir- reflexive are classified. In addition to that, more general relational structures having finitely many relations of described type are considered.
For those a classification is achieved when assuming that sets of colors assigned to pairs of vertices each one representing set of present edges between this pair constitute a linear partial order.