Almost fair perfect matchings in complete bipartite graphs

Abeer Othman, Eli Berger

Research output: Contribution to journalArticlepeer-review


Let {E1,…,Em} be a partition of E(Kn,n), where Kn,n is the complete bipartite graph, and assume that [Formula presented]. It was conjectured in [1], that there exists a perfect matching M in Kn,n with [Formula presented] In this paper, we reprove combinatorially that this conjecture is true when m=2 or m=3. This result is proved in [1] by using topological methods. In the case m=4, we prove that there is always a perfect matching M in Kn,n with s(M)≤11. We also bring here an unpublished result from 2014 of the second author of this paper together with Irine Lo and Paul Seymour, proving that there exists a function of m alone, f(m), and a perfect matching M in Kn,n such that s(M)≤f(m). This result was later reproved by Alon in [2], where an explicit formulation of f(m) was given.

Original languageEnglish
Article number113865
JournalDiscrete Mathematics
Issue number4
StatePublished - Apr 2024

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.


  • Graphs matrices
  • Latin-squares
  • Perfect-matchings

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Almost fair perfect matchings in complete bipartite graphs'. Together they form a unique fingerprint.

Cite this