Abstract

The maximum matching problem is of great interest in many areas, for example, statistical physics and theoretical computer science. However, precise determining of maximum matchings in general graphs is a challenge and calculationally intractable. In this paper, we study analytically maximum matching problem in the pseudofractal scale-free web. We derive exact expressions for size and number of maximum matchings of the network based on self-similar structure and iterative construction of network, and obtain asymptotic incremental constant for the number of maximum matchings. The obtained results are helpful to understand the structural characteristics of scale-free networks with pseudofractality.

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