Incidence complexes and r-connectedness

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.

On A System Of All Maximal Chains (Antichains) Of A Graph

Đuro Kurepa (1976)

Publications de l'Institut Mathématique

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When is a poset isomorphic to the poset of connected induced subgraphs of a graph?

Kézdy, André, Seif, Steve (1996)

Southwest Journal of Pure and Applied Mathematics [electronic only]

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The fundamental group of balanced simplicial complexes and posets.

Klee, Steven (2009)

The Electronic Journal of Combinatorics [electronic only]

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3-manifold spines and bijoins.

Luigi Grasselli (1990)

Revista Matemática de la Universidad Complutense de Madrid

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We describe a combinatorial algorithm for constructing all orientable 3-manifolds with a given standard bidimensional spine by making use of the idea of bijoin (Bandieri and Gagliardi (1982), Graselli (1985)) over a suitable pseudosimplicial triangulation of the spine.

Convex-ear decompositions and the flag $h$ -vector.

Schweig, Jay (2011)

The Electronic Journal of Combinatorics [electronic only]

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Order-theoretical connectivity.

Richmond, T.A., Vainio, R. (1990)

International Journal of Mathematics and Mathematical Sciences

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