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.
Bibliographical noteFunding Information:
This Research was supported by The Israel Science Foundation (grant number 862/10).
© 2019, The Hebrew University of Jerusalem.
ASJC Scopus subject areas
- Mathematics (all)