Authors: Dizdarević, Manuela Muzika
Živaljević, Rade 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Hamiltonian surfaces in the 4-cube, 4-bit Gray codes and Venn diagrams
Journal: Publications de l'Institut Mathematique
Volume: 111
Issue: 125
First page: 17
Last page: 40
Issue Date: 2022
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM2225017M
Abstract: 
We study Hamiltonian surfaces in the d-dimensional cube Id as intermediate objects useful for comparative analysis of Venn diagrams and Gray cycles. In particular we emphasize the importance of 0-Hamiltonian spheres and the “sphericity” of Gray codes in the context of reducible Venn diagrams. For illustration we show that precisely two, out of the nine known types of 4-bit Gray cycles, are not spherical. The unique, balanced Gray cycle is spherical, which in turn leads to a new construction of a reducible Venn diagram with 5 ellipses (originally constructed by P. Hamburger and R. E. Pippert).
Keywords: Gray cycles | Hamiltonian surfaces | Venn diagrams
Publisher: Mathematical Institute of the Serbian Academy of Sciences and Arts

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