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Article

Ayala, R. ; Chávez, M. J. ; Márquez, A. ; Quintero, A.
On the connectivity of skeletons of pseudomanifolds with boundary. (English). Mathematica Bohemica, vol. 127 (2002), issue 3, pp. 375-384
MSC: 05C40, 57M20, 57Q05 | MR 1931322 | Zbl 1003.05066 | DOI: 10.21136/MB.2002.134070
Keywords:
connectivity; graph; 2-complex; pseudomanifolds
Summary:
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.
References:
[1] R. Ayala, M. J. Chávez, A. Márquez, A. Quintero: On the connectivity of infinite graphs and 2-complexes. Discrete Math. 194 (1999), 13–37. MR 1654960
[2] D. Barnette: Decompositions of homology manifolds and their graphs. Israel J. Math. 41 (1982), 203–212. DOI 10.1007/BF02771721 | MR 0657856 | Zbl 0498.57004
[3] D. König: Theory of Finite and Infinite Graphs. Birkhäuser, 1990. MR 1035708
[4] D. G. Larman, P. Mani: On the existence of certain configuration within graphs and the 1-skeletons of polytopes. Proc. London Math. Soc. 20 (1970), 144–60. MR 0263687
[5] E. Y. Woon: $n$-connectedness in pure 2-complexes. Israel J. Math. 52 (1985), 177–192. DOI 10.1007/BF02786514 | MR 0815808 | Zbl 0593.05046
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