Abstract
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 language | English |
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Pages (from-to) | 161-167 |
Number of pages | 7 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 91 |
Issue number | 2 |
DOIs | |
State | Published - 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.