Discrete Mathematics & Theoretical Computer Science
| author: | C. R. Subramanian |
|---|---|
| title: | Paths of specified length in random k-partite graphs |
| keywords: | random graphs, paths, bijections |
| abstract: | Fix positive integers k and l.
Consider a random k-partite graph
on n vertices obtained
by partitioning the vertex set into Vi, (i=1, ... ,k) each
having size Ω(n) and choosing each possible edge with
probability p.
Consider any vertex x in any
Vi and
any vertex y. We show that the expected number of
simple paths of even length l
between x
and y differ
significantly depending on whether y belongs
to the same Vi
(as x does) or not.
A similar phenomenon occurs when l is odd.
This result holds even when k,l vary
slowly with n.
This fact has implications to coloring random graphs. The proof is
based on establishing bijections between sets of paths.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |
| reference: | C. R. Subramanian (2001), Paths of specified length in random k-partite graphs, Discrete Mathematics and Theoretical Computer Science 4, pp. 133-138 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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