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2024 | OriginalPaper | Chapter

The Spectrum Problem for the 4-Uniform 4-Colorable 3-Cycles with Maximum Degree 2

Authors : Ryan C. Bunge, Saad I. El-Zanati, Julie N. Kirkpatrick, Shania M. Sanderson, Michael J. Severino, William F. Turner

Published in: Combinatorics, Graph Theory and Computing

Publisher: Springer Nature Switzerland

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Abstract

The complete t-uniform hypergraph of order v, denoted \(K^{(t)}_v\), has a set V with v elements as its vertex set and the set of all t-element subsets of V as its edge set. For the purposes of this work, we define a 4-uniform 3-cycle of maximum degree 2 to be any 4-uniform hypergraph of maximum degree 2 that can be obtained by adding two vertices to each of the three edges in \(K^{(2)}_3\). There are five such 4-uniform hypergraphs up to isomorphism. Two of them have chromatic number 4. We give necessary and sufficient conditions for the existence of a decomposition of the complete 4-uniform hypergraph of order v into these 4-colorable 3-cycles.

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Title: The Spectrum Problem for the 4-Uniform 4-Colorable 3-Cycles with Maximum Degree 2
Authors: Ryan C. Bunge
Saad I. El-Zanati
Julie N. Kirkpatrick
Shania M. Sanderson
Michael J. Severino
William F. Turner
Publisher: Springer Nature Switzerland
Book: Combinatorics, Graph Theory and Computing
Print ISBN: 978-3-031-62165-9

Electronic ISBN: 978-3-031-62166-6

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-62166-6_18

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