## Abstract

A function diagram (f-diagram) D consists of the family of curves { 1 {combining short stroke overlay}ñ} obtained from n continuous functions f_{i}:[0,1]→R(1≤i≤n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement Ḡ is a comparability graph. An f-diagram generalizes the notion of a permulation diagram where the f_{i} are linear functions. It is also shown that G is the intersection graph of the concatenation of ≤k permutation diagrams if and only if the partial order dimension of G ̄ is ≤k+1. Computational complexity results are obtained for recognizing such graphs.

Original language | English |
---|---|

Pages (from-to) | 37-46 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 43 |

Issue number | 1 |

DOIs | |

State | Published - 1983 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics