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On connectivity of the facet graphs of simplicial complexes

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Abstract

The paper studies the connectivity properties of facet graphs of simplicial complexes of combinatorial interest. In particular, it is shown that the facet graphs of d-cycles, d-hypertrees and d-hypercuts are, respectively, (d +1)-, d-and (n − d − 1)-vertex-connected. It is also shown that the facet graph of a d-cycle cannot be split into more than s connected components by removing at most s vertices. In addition, the paper discusses various related issues, as well as an extension to cell-complexes.

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Acknowledgments

We are grateful to Roy Meshulam and Eran Nevo for enlightening discussions. Many thanks also to the anonymous referee for careful reading and numerous suggestions for improvement.

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Authors and Affiliations

  1. Department of Computer Science, University of Haifa, Haifa, 31905, Israel

    Ilan I. Newman & Yuri Rabinovich

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  1. Ilan I. Newman
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  2. Yuri Rabinovich
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Correspondence to Ilan I. Newman.

Additional information

This Research was supported by The Israel Science Foundation (grant number 862/10).

Part of this research was done while this author visited Mittag-Leffler Institute, Stockholm.

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Newman, I.I., Rabinovich, Y. On connectivity of the facet graphs of simplicial complexes. Isr. J. Math. 234, 521–545 (2019). https://doi.org/10.1007/s11856-019-1923-1

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  • DOI: https://doi.org/10.1007/s11856-019-1923-1

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