# Linear recognition of generalized Fibonacci cubes $Q_h(111)$

Abstract : The generalized Fibonacci cube $Q_h(f)$ is the graph obtained from the $h$-cube $Q_h$ by removing all vertices that contain a given binary string $f$ as a substring. In particular, the vertex set of the 3rd order generalized Fibonacci cube $Q_h(111)$ is the set of all binary strings $b_1b_2 \ldots b_h$ containing no three consecutive 1's. We present a new characterization of the 3rd order generalized Fibonacci cubes based on their recursive structure. The characterization is the basis for an algorithm which recognizes these graphs in linear time.
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Journal articles

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yoomi Rho, Aleksander Vesel. Linear recognition of generalized Fibonacci cubes $Q_h(111)$. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.349-362. ⟨10.46298/dmtcs.2165⟩. ⟨hal-01364442⟩

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