Geodesic
On the connectivity of skeletons of pseudomanifolds with boundary
Mathematica Bohemica, Tome 127 (2002) no. 3, pp. 375-384

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MR Zbl
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.
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.
DOI : 10.21136/MB.2002.134070
Classification : 05C40, 57M20, 57Q05
Keywords: connectivity; graph; 2-complex; pseudomanifolds 
Ayala, R.; Chávez, M. J.; Márquez, A.; Quintero, A. On the connectivity of skeletons of pseudomanifolds with boundary. Mathematica Bohemica, Tome 127 (2002) no. 3, pp. 375-384. doi: 10.21136/MB.2002.134070
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[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

[2] D. Barnette: Decompositions of homology manifolds and their graphs. Israel J. Math. 41 (1982), 203–212. | DOI | MR | Zbl

[3] D. König: Theory of Finite and Infinite Graphs. Birkhäuser, 1990. | MR

[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

[5] E. Y. Woon: $n$-connectedness in pure 2-complexes. Israel J. Math. 52 (1985), 177–192. | DOI | MR | Zbl

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