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Non covered vertices in Fibonacci cubes by a maximum set of disjoint hypercubes

2016/06/01 by Michel Mollard, Mollard, Michel
Computer Science · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems #Supramolecular Self-Assembly in Materials

paper · doi:10.48550/arxiv.1606.00138

openalex publication_date 2016/06/01 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28

Abstract

The Fibonacci cube of dimension n, denoted as Γ n , is the subgraph of n-cube Q n induced by vertices with no consecutive 1's. In this short note we prove that asymptotically all vertices of Γ n are covered by a maximum set of disjoint subgraphs isomorphic to Q k , answering an open problem proposed in [2].

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