On the connectivity of skeletons of pseudomanifolds with boundary

R. Ayala; M. J. Chávez; Alberto Márquez; Antonio Quintero

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 3, page 375-384
  • ISSN: 0862-7959

Abstract

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In this note we show that 1 -skeletons and 2 -skeletons of n -pseudomanifolds with full boundary are ( n + 1 ) -connected graphs and n -connected 2 -complexes, respectively. This generalizes previous results due to Barnette and Woon.

How to cite

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Ayala, R., et al. "On the connectivity of skeletons of pseudomanifolds with boundary." Mathematica Bohemica 127.3 (2002): 375-384. <http://eudml.org/doc/249066>.

@article{Ayala2002,
abstract = {In this note we show that $1$-skeletons and $2$-skeletons of $n$-pseudomanifolds with full boundary are $(n+1)$-connected graphs and $n$-connected $2$-complexes, respectively. This generalizes previous results due to Barnette and Woon.},
author = {Ayala, R., Chávez, M. J., Márquez, Alberto, Quintero, Antonio},
journal = {Mathematica Bohemica},
keywords = {connectivity; graph; 2-complex; pseudomanifolds; connectivity; graph; 2-complex; pseudomanifolds},
language = {eng},
number = {3},
pages = {375-384},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the connectivity of skeletons of pseudomanifolds with boundary},
url = {http://eudml.org/doc/249066},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Ayala, R.
AU - Chávez, M. J.
AU - Márquez, Alberto
AU - Quintero, Antonio
TI - On the connectivity of skeletons of pseudomanifolds with boundary
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 3
SP - 375
EP - 384
AB - In this note we show that $1$-skeletons and $2$-skeletons of $n$-pseudomanifolds with full boundary are $(n+1)$-connected graphs and $n$-connected $2$-complexes, respectively. This generalizes previous results due to Barnette and Woon.
LA - eng
KW - connectivity; graph; 2-complex; pseudomanifolds; connectivity; graph; 2-complex; pseudomanifolds
UR - http://eudml.org/doc/249066
ER -

References

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  1. On the connectivity of infinite graphs and 2-complexes, Discrete Math. 194 (1999), 13–37. (1999) MR1654960
  2. Decompositions of homology manifolds and their graphs, Israel J. Math. 41 (1982), 203–212. (1982) Zbl0498.57004MR0657856
  3. Theory of Finite and Infinite Graphs, Birkhäuser, 1990. (1990) MR1035708
  4. On the existence of certain configuration within graphs and the 1-skeletons of polytopes, Proc. London Math. Soc. 20 (1970), 144–60. (1970) MR0263687
  5. n -connectedness in pure 2-complexes, Israel J. Math. 52 (1985), 177–192. (1985) Zbl0593.05046MR0815808

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