7 research outputs found
The complexity of counting surjective homomorphisms and compactions
A homomorphism from a graph to a graph is a function from the vertices of to the vertices of that preserves edges. A homomorphism is surjective if it uses all of the vertices of , and it is a compaction if it uses all of the vertices of and all of the nonloop edges of . Hell and Nešetřil gave a complete characterization of the complexity of deciding whether there is a homomorphism from an input graph to a fixed graph . A complete characterization is not known for surjective homomorphisms or for compactions, though there are many interesting results. Dyer and Greenhill gave a complete characterization of the complexity of counting homomorphisms from an input graph to a fixed graph . In this paper, we give a complete characterization of the complexity of counting surjective homomorphisms from an input graph to a fixed graph , and we also give a complete characterization of the complexity of counting compactions from an input graph to a fixed graph . In an addendum we use our characterizations to point out a dichotomy for the complexity of the respective approximate counting problems (in the connected case)
The Complexity of Counting Surjective Homomorphisms and Compactions
A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices
of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a
compaction if it uses all of the vertices of H and all of the non-loop edges of H. Hell and Neˇsetˇril gave a
complete characterisation of the complexity of deciding whether there is a homomorphism from an input
graph G to a fixed graph H. A complete characterisation is not known for surjective homomorphisms or
for compactions, though there are many interesting results. Dyer and Greenhill gave a complete characterisation
of the complexity of counting homomorphisms from an input graph G to a fixed graph H. In
this paper, we give a complete characterisation of the complexity of counting surjective homomorphisms
from an input graph G to a fixed graph H and we also give a complete characterisation of the complexity
of counting compactions from an input graph G to a fixed graph H
The complexity of counting surjective homomorphisms and compactions
A homomorphism from a graph to a graph is a function from the vertices of to the vertices of that preserves edges. A homomorphism is surjective if it uses all of the vertices of , and it is a compaction if it uses all of the vertices of and all of the nonloop edges of . Hell and Nešetřil gave a complete characterization of the complexity of deciding whether there is a homomorphism from an input graph to a fixed graph . A complete characterization is not known for surjective homomorphisms or for compactions, though there are many interesting results. Dyer and Greenhill gave a complete characterization of the complexity of counting homomorphisms from an input graph to a fixed graph . In this paper, we give a complete characterization of the complexity of counting surjective homomorphisms from an input graph to a fixed graph , and we also give a complete characterization of the complexity of counting compactions from an input graph to a fixed graph . In an addendum we use our characterizations to point out a dichotomy for the complexity of the respective approximate counting problems (in the connected case)
The complexity of counting surjective homomorphisms and compactions
A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices
of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a
compaction if it uses all of the vertices of H and all of the non-loop edges of H. Hell and Neˇsetˇril gave a
complete characterisation of the complexity of deciding whether there is a homomorphism from an input
graph G to a fixed graph H. A complete characterisation is not known for surjective homomorphisms or
for compactions, though there are many interesting results. Dyer and Greenhill gave a complete characterisation
of the complexity of counting homomorphisms from an input graph G to a fixed graph H. In
this paper, we give a complete characterisation of the complexity of counting surjective homomorphisms
from an input graph G to a fixed graph H and we also give a complete characterisation of the complexity
of counting compactions from an input graph G to a fixed graph H
The complexity of counting surjective homomorphisms and compactions
A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a compaction if it uses all of the vertices of H and all of the non-loop edges of H. Hell and Neˇsetˇril gave a complete characterisation of the complexity of deciding whether there is a homomorphism from an input graph G to a fixed graph H. A complete characterisation is not known for surjective homomorphisms or for compactions, though there are many interesting results. Dyer and Greenhill gave a complete characterisation of the complexity of counting homomorphisms from an input graph G to a fixed graph H. In this paper, we give a complete characterisation of the complexity of counting surjective homomorphisms from an input graph G to a fixed graph H and we also give a complete characterisation of the complexity of counting compactions from an input graph G to a fixed graph H