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Zunaira Kosar

Publications and source records attributed to Zunaira Kosar.

5 recordsLinked to original sources
arXiv2017

An Efficient Algebraic Criterion for Shellability

In this paper, we give a new and efficient algebraic criterion for the pure as well as non-pure shellability of simplicial complex $Δ$ over [n]. We also give an algebraic characterization of a leaf in a simplicial complex (defined in [8]). Moreover, we introduce the concept of Gallai-simplicial complex $Δ_Γ(G)$ of a finite simple graph G. As an application, we show that the face ring of the Gallai simplicial complex associated to tree is Cohen-Macaulay.

math.AC↗
arXiv2017

Nested Artin Strong Approximation Property

We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.

math.AC↗
arXiv2017

Linear Residuals and Gallai-Simplicial Complexes

In this paper, we give a new algebraic criterion for the {\em shellability} of (non-pure) simplicial complex $Δ$ over $[n]$, shellable in the sense of Björner and Wachs \cite{BW}. We show that the spanning simplicial complex of doubly uni-cyclic graph is non-pure shellable. Moreover, we introduce the concept of Gallai-simplicial complex $Δ_Γ(G)$ of a finite simple graph $G$. We applied the obtained criterion to discuss the shellability of Gallai simplicial complexes associated to various classes of graphs..

math.AC↗