Editing Graph homomorphism (section)

===Variants===
General homomorphisms can also be thought of as a kind of coloring: if the vertices of a fixed graph ''H'' are the available ''colors'' and edges of ''H'' describe which colors are ''compatible'', then an ''H''-coloring of ''G'' is an assignment of colors to vertices of ''G'' such that adjacent vertices get compatible colors.
Many notions of graph coloring fit into this pattern and can be expressed as graph homomorphisms into different families of graphs.
[[Circular coloring]]s can be defined using homomorphisms into [[circular clique|circular complete graph]]s, refining the usual notion of colorings.{{sfnm|1a1=Hell|1a2=Nešetřil|1y=2004|1loc=§6.1|2a1=Hahn|2a2=Tardif|2y=1997|2loc=§4.4}}
[[Fractional coloring|Fractional]] and [[Fractional coloring#Definitions|''b''-fold coloring]] can be defined using homomorphisms into [[Kneser graph]]s.{{sfnm|1a1=Hell|1a2=Nešetřil|1y=2004|1loc=§6.2|2a1=Hahn|2a2=Tardif|2y=1997|2loc=§4.5}}
[[T-coloring]]s correspond to homomorphisms into certain infinite graphs.{{sfn|Hell|Nešetřil|2004|loc=§6.3}}
An [[oriented coloring]] of a directed graph is a homomorphism into any [[oriented graph]].{{sfn|Hell|Nešetřil|2004|loc=§6.4}}
An [[L(2,1)-coloring]] is a homomorphism into the [[complement graph|complement]] of the [[path graph]] that is locally injective, meaning it is required to be injective on the neighbourhood of every vertex.<ref>{{citation|first1=J.|last1=Fiala|first2=J.|author2-link=Jan Kratochvíl|last2=Kratochvíl|s2cid=17507393|title=Partial covers of graphs|year=2002|journal=Discussiones Mathematicae Graph Theory|volume=22|issue=1|pages=89–99|doi=10.7151/dmgt.1159}}</ref>