Colorings of the d-regular infinite tree

Shlomo Hoory*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The existence of small d-regular graphs of a prescribed girth g is equivalent to the existence of certain codes in the d-regular infinite tree. We show that in the tree "perfect" codes exist, but those are usually not "graphic". We also give an explicit coloring that is "nearly perfect" as well as "nearly graphic".

Original languageAmerican English
Pages (from-to)161-167
Number of pages7
JournalJournal of Combinatorial Theory. Series B
Issue number2
StatePublished - Jul 2004

Bibliographical note

Funding Information:
·Present address: Department of Computer Science, University of Toronto, Toronto, ON, Canada. E-mail addresses: [email protected], [email protected] (S. Hoory), [email protected] (N. Linial). 1Supported in part by grants from the US-Israel Binational Science Fund and from the Israeli Academy of Science.


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