An Algorithmic Embedding of Graphs via Perfect Matchings

  • Vojtech Rödl
  • Andrzej Ruciński
  • Michelle Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1518)


Recently Komlós, Sárközy, and Szemerédi proved a striking result called the blow-up lemma that, loosely speaking, enables one to embed any bounded degree graph H as a spanning subgraph of an e-regular graph G. The first proof given by Komlós, Sárközy, and Szemerédi was based on a probabilistic argument [8]. Subsequently, they derandomized their approach to provide an algorithmic embedding in [9]. In this paper we give a different proof of the algorithmic version of the blow-up lemma. Our approach is based on a derandomization of a probabilistic proof of the blow-up lemma given in [13]. The derandomization utilizes the Erdös-Selfridge method of conditional probabilities and the technique of pessimistic estimators.


Bipartite Graph Perfect Match Regular Graph Algorithmic Version Regularity Lemma 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Vojtech Rödl
    • 1
  • Andrzej Ruciński
    • 1
  • Michelle Wagner
    • 1
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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