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Circuit Decompositions and Shortest Circuit Coverings of Hypergraphs

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Abstract

It is one of fundamental theorems in graph theory that every even graph has a circuit decomposition. This classical result for ordinary graphs is extended in this paper for uniform bridgeless hypergraphs if the degree of every vertex is even. One of major open problems for shortest circuit cover was a conjecture proposed by Itai and Rodeh (Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 62, pp. 289–299. Springer, Berlin, 1978) that every bridgeless graph G has a circuit cover of total length at most \(|E|+|V|-1\). This conjecture was solved by Fan (J Combin Theory Ser B 74:353–367, 1998) for ordinary graphs, and is extended in this paper for bridgeless hypergraphs.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Liying Kang

  2. College of Arts and Sciences, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China

    Weihua Lu

  3. Ocean College, Zhejiang University, Zhoushan, 316021, Zhejiang, People’s Republic of China

    Yezhou Wu

  4. Department of Mathematical Sciences and Center for Computational Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Dong Ye

  5. Department of Mathematics, West Virginia University, Morgantown, WV, 26506, USA

    Cun-Quan Zhang

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  1. Liying Kang
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  2. Weihua Lu
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  4. Dong Ye
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  5. Cun-Quan Zhang
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Corresponding author

Correspondence to Cun-Quan Zhang.

Additional information

Liying Kang: Partially supported by National Natural Science Foundation of China (Nos. 11471210 and 11571222). Yezhou Wu: Partially supported by National Natural Science Foundation of China (No. 11501504) and Natural Science Foundation of Zhejiang Province (No. LY16A010005). Dong Ye: Partially supported by Simons Foundation (No. 396516). Cun-Quan Zhang: Partially supported by National Security Agency (No. H98230-16-1-0004) and National Science Foundation (No. DMS-1700218).

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Kang, L., Lu, W., Wu, Y. et al. Circuit Decompositions and Shortest Circuit Coverings of Hypergraphs. Graphs and Combinatorics 34, 365–372 (2018). https://doi.org/10.1007/s00373-018-1881-0

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  • DOI: https://doi.org/10.1007/s00373-018-1881-0

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