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In this paper, we determine the tight upper bound for the number of matchings of connected $n$-vertex tricyclic graphs. We show that this bound is $13 f_{n-4} + 16f_{n-5}$, where $f_n$ be the  $n$th Fibonacci number. We also  characterize the $n$-vertex simple connected tricyclic graph for which the bound is best  possible. A corrigendum was added to this paper on Jun 17, 2015.

The Tight Upper Bound for the Number of Matchings of Tricyclic Graphs