# Discrete Mathematics & Theoretical Computer Science

## Volume 4 n° 2 (2001), pp. 133-138

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 V each
having size _{i}, (i=1, ... ,k)Ω(n) and choosing each possible edge with
probability p.
Consider any vertex x in any
V and
any vertex _{i}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 V
(as _{i}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.
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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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