Monotone paths in edge-ordered sparse graphs

Yehuda Roditty, Barack Shoham, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)411-417
Number of pages7
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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