On connectivity of the facet graphs of simplicial complexes

Ilan I. Newman; Yuri Rabinovich

doi:10.1007/s11856-019-1923-1

On connectivity of the facet graphs of simplicial complexes

Ilan I. Newman, Yuri Rabinovich

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	521-545
Number of pages	25
Journal	Israel Journal of Mathematics
Volume	234
Issue number	2
DOIs	https://doi.org/10.1007/s11856-019-1923-1
State	Published - 1 Oct 2019

Bibliographical note

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

Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1007/s11856-019-1923-1

Cite this

@article{23c35d2cf3234ab786ee070a349a556f,

title = "On connectivity of the facet graphs of simplicial complexes",

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.",

author = "Newman, {Ilan I.} and Yuri Rabinovich",

note = "Funding Information: This Research was supported by The Israel Science Foundation (grant number 862/10). Publisher Copyright: {\textcopyright} 2019, The Hebrew University of Jerusalem.",

year = "2019",

month = oct,

day = "1",

doi = "10.1007/s11856-019-1923-1",

language = "English",

volume = "234",

pages = "521--545",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - On connectivity of the facet graphs of simplicial complexes

AU - Newman, Ilan I.

AU - Rabinovich, Yuri

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85073984380&partnerID=8YFLogxK

U2 - 10.1007/s11856-019-1923-1

DO - 10.1007/s11856-019-1923-1

M3 - Article

AN - SCOPUS:85073984380

SN - 0021-2172

VL - 234

SP - 521

EP - 545

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

On connectivity of the facet graphs of simplicial complexes

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this