1 research outputs found
Homomorphism-homogeneous L-colored graphs
A relational structure is homomorphism-homogeneous (HH-homogeneous for short)
if every homomorphism between finite induced substructures of the structure can
be extended to a homomorphism over the whole domain of the structure.
Similarly, a structure is monomorphism-homogeneous (MH-homogeneous for short)
if every monomorphism between finite induced substructures of the structure can
be extended to a homomorphism over the whole domain of the structure. In this
paper we consider L-colored graphs, that is, undirected graphs without loops
where sets of colors selected from L are assigned to vertices and edges. A full
classification of finite MH-homogeneous L-colored graphs where L is a chain is
provided, and we show that the classes MH and HH coincide. When L is a diamond,
that is, a set of pairwise incomparable elements enriched with a greatest and a
least element, the situation turns out to be much more involved. We show that
in the general case the classes MH and HH do not coincide.Comment: Submitted to European Journal of Combinatoric