Mahesh Ramani

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math.CO2026

Linear Tur'an Numbers of Four-Edge Uniform Paths via Incidence Rank

Mahesh Ramani

Let $P_{4}^{r}$ denote the $r$ -uniform expansion of the graph path with four edges. We prove that every $n$ -vertex linear $r$ -uniform $P_{4}^{r}$ -free hypergraph has at most $(r + 1) n / r$ edg…

math.CO2026

Incidence Rank and Bounded Defect for Linear Hypergraphs with Cograph Line Graphs

Mahesh Ramani

Let $N (H)$ be the edge--vertex incidence matrix of a finite linear $s$ -uniform hypergraph whose line graph is a cograph, and define \[ R_s(H)=(s+1)\operatorname{rank}_{\mathbb R}N(…

math.CO2026

Blocking Amalgamations, Maximal Arcs, and Generalized Crowns

Mahesh Ramani

Let $C_{1, k}^{r}$ be the $r$ -uniform $k$ -crown and put $h = r - k + 2$ . For a finite linear intersecting $r$ -uniform hypergraph $G$ , let $τ_{h} (G)$ be the minimum size of a set meeting every…

math.CO2026

Robust Repulsion for Growing Crowns in Linear Hypergraphs

Mahesh Ramani

Put $q = r - 1$ , $t = k - 1$ , and $D = tq + 1$ . For an edge $e$ of a linear $C_{1, k}^{r}$ -free $r$ -uniform hypergraph, define \[ δ_H(e)=\sum_{v\in e}\frac{1}{d_H(v)}-\frac{r}{D}. \] The defect s…

math.CO2026

A Matrix-Degree Obstruction to Rational Generation of Boolean-Lattice Pseudo-Roots

Mahesh Ramani

For the neighborhood seed associated with the four-vertex path $P_{4}$ , the diamond operations do not recover all Boolean-lattice pseudo-roots. The corresponding question for unrestr…

math.CO2026

Cographs and Minimum Diamond-Generating Edge Sets in Boolean Lattices

Mahesh Ramani

We study a local closure operation on the cover edges of a Boolean lattice: whenever the two lower edges or the two upper edges of a square face are present, all four edges of that…

math.CO2026

Spectral Theory of the Toroidal 3D Queen Graph

Mahesh Ramani

We study the adjacency spectrum of the toroidal three-dimensional queen graph $G_{n}$ on $(Z_{n})^{3}$ . Since $G_{n}$ is a Cayley graph on an abelian group, its adjacency matrix i…

math.CO2026

On the Structure of 3D Queen Domination

Mahesh Ramani

We study the domination number $γ (Q_{n}^{3})$ of the three-dimensional $n \times n \times n$ queen graph. The main result is a stratified theorem computing, for each position type -- c…