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 Pk=1: v1, v2,..., vk+1 in G such that either, f((vi, vi+1)) < f((Vi+1,Vi+2)) or f((vivi+1)) > f((vi+1, vi+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 |
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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