Geodesic
Finite free resolutions and 1-skeletons of simplicial complexes
Journal of Algebraic Combinatorics, Tome 6 (1997) no. 1, pp. 89-93.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A technique of minimal free resolutions of Stanley-Reisner rings enables us to show the following two results: (1) The 1-skeleton of a simplicial $( d-1)$-sphere is $d$-connected, which was first proved by Barnette; (2) The comparability graph of a non-planar distributive lattice of rank $d-1$ is $d$-connected.
Keywords: simplicial complex, 1-skeleton, comparability graph, $d$-connected, free resolution 
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     title = {Finite free resolutions and 1-skeletons of simplicial complexes},
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Terai, Naoki; Hibi, Takayuki. Finite free resolutions and 1-skeletons of simplicial complexes. Journal of Algebraic Combinatorics, Tome 6 (1997) no. 1, pp. 89-93. http://geodesic.mathdoc.fr/item/JAC_1997__6_1_a0/