Author

Mahesh Ramani

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Preprint Aug 2026

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

Let $N(H)$ be the edge--vertex incidence matrix of a finite linear $s$-uniform hypergraph whose line graph is a cograph, and define \[ R_s(H)=(s+1)\operatorname{rank}_{\mathbb R}N(H)-s|E(H)|. \] The inequality $R_s(H)\ge0$ holds, with equality characterized by affine planes of order $s$ on every row-dependent component...

Mahesh Ramani · 0 citations

Preprint Aug 2026

Blocking Amalgamations, Maximal Arcs, and Generalized Crowns

Let $C^r_{1,k}$ be the $r$-uniform $k$-crown and put $h=r-k+2$. For a finite linear intersecting $r$-uniform hypergraph $G$, let $\tau_h(G)$ be the minimum size of a set meeting every edge of $G$ in at least $h$ vertices, and define \[ \rho_{r,k}=\sup_G\frac{|E(G)|}{\tau_h(G)}. \] We prove that every fixed pair $(G,B)$...

Mahesh Ramani · 0 citations

Preprint Aug 2026

Robust Repulsion for Growing Crowns in Linear Hypergraphs

Put $q=r-1$, $t=k-1$, and $D=tq+1$. For an edge $e$ of a linear $C^r_{1,k}$-free $r$-uniform hypergraph, define \[ \delta_H(e)=\sum_{v\in e}\frac{1}{d_H(v)}-\frac{r}{D}. \] The defect satisfies $\delta_H(e)\ge 0$. At equality, every vertex of $e$ has degree $D$, and the petal trace at $e$ is a disjoint union of $t$ aff...

Mahesh Ramani · 0 citations