, Volume 19, Issue 3, pp 437–452 | Cite as

Perfect Matchings in ε-Regular Graphs and the Blow-Up Lemma

  • Vojtech Rödl
  • Andrzej Ruciński
Original Paper


on vertex set \(\), \(\), with density d>2ε and all vertex degrees not too far from d, has about as many perfect matchings as a corresponding random bipartite graph, i.e. about \(\).

In this paper we utilize that result to prove that with probability quickly approaching one, a perfect matching drawn randomly from G is spread evenly, in the sense that for any large subsets of vertices \(\) and \(\), the number of edges of the matching spanned between S and T is close to |S||T|/n (c.f. Lemma 1).

As an application we give an alternative proof of the Blow-up Lemma of Komlós, Sárközy and Szemerédi [10].

AMS Subject Classification (1991) Classes:  05C75 


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Copyright information

© János Bolyai Mathematical Society, 1999

Authors and Affiliations

  • Vojtech Rödl
    • 1
  • Andrzej Ruciński
    • 2
  1. 1.Department of Mathematics and Computer Science, Emory University; Atlanta, GA 30322, USA; E-mail: rodl@mathcs.emory.eduUS
  2. 2.Department of Discrete Mathematics, Adam Mickiewicz University; Poznań, Poland; E-mail:

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