Random Graph-Homomorphisms and Logarithmic Degree

@inproceedings{Benjamini2006RandomGA,
  title={Random Graph-Homomorphisms and Logarithmic Degree},
  author={Itai Benjamini},
  year={2006}
}
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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References

Publications referenced by this paper.
Showing 1-8 of 8 references

Range of cube-indexed random walks

  • J. Kahn
  • Israel Journal of Mathematics 124
  • 2001
Highly Influential
4 Excerpts

Random Surfaces

  • S. Sheffield
  • Asterisque, no. 304
  • 2005
1 Excerpt

Tree-indexed random walks on groups and first passage percolation

  • I. Benjamini, Y. Peres
  • Probability Theory and Related Fields, 98
  • 1994
1 Excerpt

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