Ramsey numbers for degree monotone paths

Yair Caro, Raphael Yuster, Christina Zarb

Research output: Contribution to journalArticlepeer-review


A path v1,v2,…,vm in a graph G is degree-monotone if deg(v1)≤deg(v2)≤⋯≤deg(vm) where deg(vi) is the degree of vi in G. Longest degree-monotone paths have been studied in several recent papers. Here we consider the Ramsey type problem for degree monotone paths. Denote by Mk(m) the minimum number M such that for all n≥M, in any k-edge coloring of Kn there is some 1≤j≤k such that the graph formed by the edges colored j has a degree-monotone path of order m. We prove several nontrivial upper and lower bounds for Mk(m).

Original languageEnglish
Pages (from-to)124-131
Number of pages8
JournalDiscrete Mathematics
Issue number2
StatePublished - 6 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.


  • Degrees
  • Paths
  • Ramsey

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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