We deal with two very related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph "resembles" a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs. Concerning regular partitions, we present a novel concept of regularity that takes into account the graph's degree distribution, and show that if G = (V, E) satisfies a certain boundedness condition, then G admits a regular partition. In addition, building on the work of Alon and Naor [4], we provide an algorithm that computes a regular partition of a given (possibly sparse) graph G in polynomial time. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Alon, N., Coja-Oghlan, A., Hàn, H., Kang, M., Rödl, V., & Schacht, M. (2007). Quasi-randomness and algorithmic regularity for graphs with general degree distributions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4596 LNCS, pp. 789–800). Springer Verlag. https://doi.org/10.1007/978-3-540-73420-8_68
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