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The Journal of Supercomputing
Published in: The Journal of Supercomputing 14/2023

23-04-2023

On forcibly k-edge-connected and forcibly super edge-connected uniform hypergraphic sequences

Authors: Xuemei Liu, Jixiang Meng, Yingzhi Tian

Published in: The Journal of Supercomputing | Issue 14/2023

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Abstract

We give simple sufficient degree conditions for uniform hypergraphs to be k-edge-connected or super edge-connected and strongest monotone increasing degree conditions for uniform hypergraphs to be k-edge-connected when \(k=1,2,3\). As corollaries, we obtain the sufficient degree conditions for k-edge-connected graphs given by Bauer et al. (Networks 54(2):95–98, 2009) and the minimum degree conditions for maximally edge-connected (Chartrand, SIAM J Appl Math 14(4):778–781, 1966; Dankelmann and Meierling, Discrete Math 339(2):33–38, 2016) and super edge-connected (Kelman, Theory Probab Appl 17(2):243–254, 1972; Zhao et al., Graphs Combin 36(4):1065–1078, 2020) uniform hypergraphs.
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Literature
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Bauer D, Hakimi SL, Kahl N, Schmeichel E (2009) Sufficient degree conditions for \(k\)-edge-connectedness of a graph. Networks 54(2):95–98MathSciNetCrossRefMATH
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Berge C (1989) Hypergraphs: Combinatorics of Finite Sets. North-Holland, AmsterdamMATH
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Kelman AK (1972) Asymptonic formulas for the probability of \(k\)-connectedness of random graphs. Theory Probab Appl 17(2):243–254
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Liu XM, Meng JX, Tian YZ (2022) On forcibly \(k\)-connected and forcibly \(k\)-arc-connected digraphic sequences. Discrete Appl Math 321:10–18MathSciNetCrossRefMATH
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Liu XM, Meng JX, Tian YZ (2022) On forcibly \(k\)-connected uniform hypergraphic sequences. (submitted for publication)
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Nash-Williams CSJA (1971) Hamiltonian arcs and circuits. In: Recent Trends in Graph Theory Lecture Notes in Mathematics. Springer, pp 197–210
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Yin JH, Guo JY (2022) A new sufficient degree condition for a graphic sequence to be forcibly \(k\)-edge-connected. Acta Math Appl Sinica (Engl Ser) 38(1):223–228MathSciNetCrossRefMATH
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Zhao S, Meng JX (2018) Sufficient conditions for hypergraphs to be maximally edge-connected hypergraphs. Appl Math Comput 333:362–368MathSciNetCrossRefMATH
20.
Zhao S, Tian YZ, Meng JX (2020) Degree sequence conditions for maximally edge-connected and super edge-connected hypergraphs. Graphs Combin 36(4):1065–1078MathSciNetCrossRefMATH
Metadata
Title
On forcibly k-edge-connected and forcibly super edge-connected uniform hypergraphic sequences
Authors
Xuemei Liu
Jixiang Meng
Yingzhi Tian
Publication date
23-04-2023
Publisher
Springer US
Published in
The Journal of Supercomputing / Issue 14/2023
Print ISSN: 0920-8542
Electronic ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-023-05287-z

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