Rutuja Sawant

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math.CO2026

On a complete characterization of path-free complexes associated with complete multipartite graphs

Priyavrat Deshpande, Shuchita Goyal, Rutuja Sawant

Let $G$ be a graph and let $\PF_t(G)$ denote the simplicial complex whose faces are vertex subsets whose induced subgraphs contain no path on $t$ vertices. These complexes encode a…

math.CO2026

On the Vertex Decomposability of $r$ -Independence Complexes of Trees

Rutuja Sawant

Let $G$ be a graph and $r \geq 1$ . A vertex subset is $r$ -independent if every connected component of its induced subgraph has size at most $r$ . The family of all such subsets forms…

math.CO2026

Homogenized Graphical Shi Arrangements and Deformed Dumont Permutations

Sauvik Poddar, Rutuja Sawant, Umesh Shankar

We introduce the homogenized graphical Shi arrangement associated with a simple undirected graph $G$ , which serves as a broad generalization of classical deformations of the braid…

math.CO2026

Vertex decomposable complexes of directed forests, conflict graphs and chordality

Priyavrat Deshpande, Rutuja Sawant

Let $D$ be a multidigraph. We study the simplicial complex $Dlf (D)$ , whose vertices are the directed edges of $D$ and whose faces correspond to directed linear forests, th…

math.CO2025

The complex of $r$ -co-connected subgraphs, chordality and Fröberg's theorem

Priyavrat Deshpande, Amit Roy, Rutuja Sawant

We introduce a new family of pure simplicial complexes, called the $r$ -co-connected complex of $G$ with respect to $A$ , $Σ_{r} (A, G)$ , where $r \geq 1$ is a natural number, $G$ is a si…

On a complete characterization of path-free complexes associated with complete multipartite graphs

On the Vertex Decomposability of r-Independence Complexes of Trees

Homogenized Graphical Shi Arrangements and Deformed Dumont Permutations

Vertex decomposable complexes of directed forests, conflict graphs and chordality

The complex of r-co-connected subgraphs, chordality and Fröberg's theorem

On the Vertex Decomposability of $r$ -Independence Complexes of Trees

The complex of $r$ -co-connected subgraphs, chordality and Fröberg's theorem