Indexing metadata

Random Graph-Homomorphisms and Logarithmic Degree


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Random Graph-Homomorphisms and Logarithmic Degree
 
2. Creator Author's name, affiliation, country Itai Benjamini; Weizmann Institute
 
2. Creator Author's name, affiliation, country Ariel Yadin; Weizmann Institute
 
2. Creator Author's name, affiliation, country Amir Yehudayoff; Weizmann Institute
 
3. Subject Discipline(s)
 
3. Subject Keyword(s)
 
3. Subject Subject classification 60C05
 
4. Description Abstract

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 typical homomorphism is bounded. In particular, a sharp transition is shown for a specific family of graphs $C_{n,k}$ (which is the tensor product of the $n$-cycle and a complete graph, with self-loops, of size $k$). That is, given any function $\psi(n)$ tending to infinity, the range of a typical homomorphism of $C_{n,k}$ is super-constant for $k= 2\log(n) - \psi(n)$, and is $3$ for $k= 2\log(n) + \psi(n)$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2007-06-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/427
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-427
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.