## Abstract

An edge-ordered graph is an ordered pair (G,f), where G = G(V,E) is a graph and f is a bijective function, f : E(G) → {1,2,..., |E(G)|}. f is called an edge ordering of G. A monotone path of length k in (G, f) is a simple path P_{k=1}: v_{1}, v_{2},..., v_{k+1} in G such that either, f((v_{i}, v_{i+1})) < f((V_{i+1},V_{i+2})) or f((v_{i}v_{i+1})) > f((v_{i+1}, v_{i+2})) for i = 1,2,..., k - 1. Given an undirected graph G, denote by α(G) the minimum over all edge orderings of the maximum length of a monotone path. In this paper we give bounds on α(G) for various families of sparse graphs, including trees, planar graphs and graphs with bounded arboricity.

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

Pages (from-to) | 411-417 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 226 |

Issue number | 1-3 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics