An Algorithmic Embedding of Graphs via Perfect Matchings

Recently Komlos, Sarkozy, and Szemeredi 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 Ɛ-regular graph G. The first proof given by Komlos, Sarkozy, and Szemeredi 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 Erdos-Selfridge method of conditional probabilities and the technique of pessimistic estimators.

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