13 papers
VascuSR: Iterative Anatomy-Aware Diffusion for CT Super-Resolution
Hairong Ni, Jiahe Huang, Minghao Guo +2
Generative super-resolution (SR) can recover sharp detail in computed tomography (CT) images from severely downsampled observations, but the missing high-frequency content is not u…
On Eternal Connected Vertex Cover
Rajat Adak, Saraswati Girish Nanoti
For a connected graph with at least one edge, the \textit{eternal connected vertex cover} number is the minimum number of guards that can maintain a connected vertex…
Linear Turán Numbers of Uniform Hypertrees
Rajat Adak, Pragya Verma
A hypergraph is linear if every pair of vertices is contained in at most one hyperedge. We study linear Turán numbers of acyclic -uniform hypergraphs, extending earlier work of…
An Upper Bound on the Linear Turán Number of -Crowns
Rajat Adak
A hypergraph is said to be \emph{linear} if every pair of vertices lies in at most one hyperedge. Given a family of -uniform hypergraphs (also called -graph…
Off-diagonal Rado numbers for and
Rajat Adak, Yash Bakshi, L. Sunil Chandran +1
The study of Ramsey-type problems for linear equations originated with Schur's theorem and was later placed in a systematic framework by Richard Rado. In the off-diagonal setting,…
Off-diagonal Rado number for and
Rajat Adak, Yash Bakshi, L. Sunil Chandran +1
Ramsey-type problems for linear equations began with Schur's theorem and were systematically generalized by Richard Rado. In the off-diagonal framework for two colors, one consider…
Bounds on Linear Turán Number for Trees
Rajat Adak, Pragya Verma
A hypergraph is said to be \emph{linear} if every pair of vertices lies in at most one hyperedge. Given a family of -uniform hypergraphs, an -uniform hyperg…
Generalized Zykov's Theorem
Rajat Adak, L. Sunil Chandran
For a simple graph , let denote its number of vertices, and let denote the number of copies of in . Zykov's theorem (1949) asserts that for any …
Vertex-Based Localization of Generalized Turán Problems
Rajat Adak, L. Sunil Chandran
Let be a family of graphs. A graph is called -free if it does not contain any member of . Generalized Turán problems aim to maximize the num…
Localization: A Framework to Generalize Extremal Graph Problems
Rajat Adak, L. Sunil Chandran
Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a f…
Vertex-Based Localization of Turán's Theorem
Rajat Adak, L. Sunil Chandran
Let be a simple graph with vertices and edges. According to Turán's theorem, if is -free, then where denotes the Turán gra…
Vertex-Based Localization of Erdős-Gallai Theorems for Paths and Cycles
Rajat Adak, L. Sunil Chandran
For a simple graph , let and denote the number of vertices and edges in , respectively. The Erdős-Gallai theorem for paths states that in a simple -free graph, $…
Revisiting Token Sliding on Chordal Graphs
Rajat Adak, Saraswati Girish Nanoti, Prafullkumar Tale
In this article, we revisit the complexity of the reconfiguration of independent sets under the token sliding rule on chordal graphs. In the \textsc{Token Sliding-Connectivity} pro…