Independent transversals in r-partite graphs

Research output: Contribution to journalArticlepeer-review


Let script G sign(r, n) denote the set of all r-partite graphs consisting of n vertices in each partite class. An independent transversal of G ∈ script G sign(r, n) is an independent set consisting of exactly one vertex from each vertex class. Let Δ(r, n) be the maximal integer such that every G ∈ script G sign(r, n) with maximal degree less than Δ(r, n) contains an independent transversal. Let Cr = limn→∞ Δ(r, n)/n. We establish the following upper and lower bounds on Cr, provided r > 2: 2[log r]-1/2[log r] - 1 ≥ Cr ≥ max {1/2e, 1/2[log(r/3)], 1/3 . 2[log r]-3}. For all r > 3, both upper and lower bounds improve upon previously known bounds of Bollobás, Erdos and Szemerédi. In particular, we obtain that C4 = 2/3, and that limr→∞ Cr ≥ 1/(2e), where the last bound is a consequence of a lemma of Alon and Spencer. This solves two open problems of Bollobás, Erdos and Szemerédi.

Original languageEnglish
Pages (from-to)255-261
Number of pages7
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 15 Nov 1997
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Independent transversals in r-partite graphs'. Together they form a unique fingerprint.

Cite this