Geodesic
Linear recognition of generalized Fibonacci cubes $Q_h(111)$
Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3.

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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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     author = {Rho, Yoomi and Vesel, Aleksander},
     title = {Linear recognition of generalized {Fibonacci} cubes $Q_h(111)$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2015-2016},
     doi = {10.46298/dmtcs.2165},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2165/}
}
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Rho, Yoomi; Vesel, Aleksander. Linear recognition of generalized Fibonacci cubes $Q_h(111)$. Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3. doi : 10.46298/dmtcs.2165. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2165/

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