Edge-ordered Ramsey numbers

Martin Balko, Máté Vizer

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We introduce and study a variant of Ramsey numbers for edge-ordered graphs, that is, graphs with linearly ordered sets of edges. The edge-ordered Ramsey number R¯e(G) of an edge-ordered graph G is the minimum positive integer N such that there exists an edge-ordered complete graph KN on N vertices such that every 2-coloring of the edges of KN contains a monochromatic copy of G as an edge-ordered subgraph of KN. We prove that the edge-ordered Ramsey number R¯e(G) is finite for every edge-ordered graph G and we obtain better estimates for special classes of edge-ordered graphs. In particular, we prove R¯e(G)≤2O(n3logn) for every bipartite edge-ordered graph G on n vertices. We also introduce a natural class of edge-orderings, called lexicographic edge-orderings, for which we can prove much better upper bounds on the corresponding edge-ordered Ramsey numbers.

Original languageEnglish
Article number103100
JournalEuropean Journal of Combinatorics
StatePublished - 1 Jun 2020
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Edge-ordered Ramsey numbers'. Together they form a unique fingerprint.

Cite this