Rajat Adak

collaborators

5 papers

math.CO2025

Generalized Zykov's Theorem

Rajat Adak, L. Sunil Chandran

For a simple graph $G$ , let $n$ denote its number of vertices, and let $N (G, K_{t})$ denote the number of copies of $K_{t}$ in $G$ . Zykov's theorem (1949) asserts that for any $K_{r + 1}$ …

math.CO2025

Vertex-Based Localization of Generalized Turán Problems

Rajat Adak, L. Sunil Chandran

Let $F$ be a family of graphs. A graph is called $F$ -free if it does not contain any member of $F$ . Generalized Turán problems aim to maximize the num…

math.CO2025

Vertex-Based Localization of Turán's Theorem

Rajat Adak, L. Sunil Chandran

Let $G$ be a simple graph with $n$ vertices and $m$ edges. According to Turán's theorem, if $G$ is $K_{r + 1}$ -free, then $m \leq ∣ E (T (n, r)) ∣,$ where $T (n, r)$ denotes the Turán gra…

math.CO2025

Vertex-Based Localization of Erdős-Gallai Theorems for Paths and Cycles

Rajat Adak, L. Sunil Chandran

For a simple graph $G$ , let $n$ and $m$ denote the number of vertices and edges in $G$ , respectively. The Erdős-Gallai theorem for paths states that in a simple $P_{k}$ -free graph, $…

cs.DS2025

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…