### Abstract

The index of an irreflexive binary relation R is the smallest cardinal number σ(R) such that R equals the union of σ(R) partial orders. With s(n) the largest index for an R defined on n points, it is shown that s(n)/log_{2} n→1 as n →∞. The index function is examined for symmetric R’s and almost transitive R’s, and a characterization for σ(R)≦2 is presented. It is shown also that inf{n:s(n)>3}≦13, but the exact value of inf {n:s(n)>3} is presently unknown.

Original language | English (US) |
---|---|

Pages (from-to) | 149-161 |

Number of pages | 13 |

Journal | Pacific Journal of Mathematics |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1971 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Directed graphs as unions of partial orders'. Together they form a unique fingerprint.

## Cite this

Fishburn, P. C., & Spencer, J. H. (1971). Directed graphs as unions of partial orders.

*Pacific Journal of Mathematics*,*39*(1), 149-161. https://doi.org/10.2140/pjm.1971.39.149