We model physical systems with ``hard constraints'' by the space Hom(G, H) of homomorphisms from a locally finite graph G to a fixed finite constraint graph H. For any assignment \* of positive real activities to the nodes of H, there is at least one Gibbs measure on Hom(G, H); when G is infinite, t
On homomorphic images of transition graphs
β Scribed by Michael Yoeli; Abraham Ginzburg
- Publisher
- Elsevier Science
- Year
- 1964
- Tongue
- English
- Weight
- 296 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0016-0032
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In this paper we investigate homomorphisms on the state behavior of linear machines and characterize their homomorphic images. These results are then applied to characterize those nonlinear machines which can be realized by larger linear machines.
## Abstract Let hom (__G, H__) be the number of homomorphisms from a graph __G__ to a graph __H__. A wellβknown result of LovΓ‘sz states that the function hom (Β·, __H__) from all graphs uniquely determines the graph __H__ up to isomorphism. We study this function restricted to smaller classes of gra
Given a bipartite connected finite graph G=(V, E) and a vertex v 0 # V, we consider a uniform probability measure on the set of graph homomorphisms f : V Γ Z satisfying f (v 0 )=0. This measure can be viewed as a G-indexed random walk on Z, generalizing both the usual time-indexed random walk and tr