Random Graph-Homomorphisms and Logarithmic Degree

  title={Random Graph-Homomorphisms and Logarithmic Degree},
  author={Itai Benjamini},
A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the infinite line Z. It is shown that if the maximal degree of G is ‘sub-logarithmic’, then the range of such a homomorphism is super-constant. Furthermore, some examples are provided, suggesting that perhaps for graphs with super-logarithmic degree, the range of a… CONTINUE READING
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