Linear recognition of generalized Fibonacci cubes $Q_h(111)

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...

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Bibliographic Details
Published inDiscrete mathematics and theoretical computer science Vol. 17 no. 3; no. Graph Theory; pp. 349 - 362
Main Authors Rho, Yoomi, Vesel, Aleksander
Format Journal Article
LanguageEnglish
Published DMTCS 03.09.2016
Discrete Mathematics & Theoretical Computer Science
Subjects
3rd order generalized fibonacci cube
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
characterization
Computer Science
Discrete Mathematics
generalized fibonacci cube
recognition algorithm
recognition algorithm
generalized Fibonacci cube
3rd order generalized Fibonacci cube
characterization
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Summary: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2165