## Abstract

Let G be a simple graph. A function f from the set of orientations of G to the set of non-negative integers is called a continuous function on orientations of G if, for any two orientations O_{1} and O_{2} of G, |f(O_{1}) - f(O_{2})| ≤ 1 whenever O_{1} and O_{2} differ in the orientation of exactly one edge of G. We show that any continuous function on orientations of a simple graph G has the interpolation property as follows: If there are two orientations O_{1} and O_{2} of G with f(O_{1}) = p and f(O_{2}) = q, where p < q, then for any integer k such that p < k < q, there are at least m orientations O of G satisfying f(O) = k, where m equals the number of edges of G. It follows that some useful invariants of digraphs including the connectivity, the arcconnectivity and the absorption number, etc., have the above interpolation property on the set of all orientations of G.

Original language | English (US) |
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Pages (from-to) | 433-438 |

Number of pages | 6 |

Journal | Czechoslovak Mathematical Journal |

Volume | 48 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1998 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)