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Shellability of 3-cut complexes of powers of cycle graphs
Pratiksha Chauhan, Samir Shukla
In connection with commutative algebra, Bayer et al. introduced cut complexes in [Topology of cut complexes of graphs, SIAM J.\ Discrete Math., 38(2):1630-1675, 2024]. For a positi…
Total -cut complexes of powers of cycle graphs and Cartesian products of certain graphs
Pratiksha Chauhan, Samir Shukla, Kumar Vinayak
For a positive integer , the \emph{ total -cut complex} of a graph , denoted as , is the simplicial complex whose facets are such that $|σ| = |…
On the Vietoris-Rips Complexes of Integer Lattices
Raju Kumar Gupta, Sourav Sarkar, Samir Shukla
For a metric space and , the Vietoris-Rips complex is a simplicial complex whose simplices are finite subsets of with diameter at most . Vi…
Distance -domination number and -independence complexes of graphs
Priyavrat Deshpande, Samir Shukla, Anurag Singh
For , the -independence complex of a graph , denoted Ind, is a simplicial complex whose faces are subsets such that each component of the i…
Neighborhood complexes, homotopy test graphs and a contribution to a conjecture of Hedetniemi
Samir Shukla
The neighborhood complex of a graph were introduced by L. Lov{á}sz in his proof of Kneser conjecture. He proved that for any graph , \begin{align} \label{abstract} χ…
Spectral gap bounds for the simplicial Laplacian and an application to random complexes
Samir Shukla, D. Yogeshwaran
In this article, we derive two spectral gap bounds for the reduced Laplacian of a general simplicial complex. Our two bounds are proven by comparing a simplicial complex in two dif…