Author

Amrit Kandasamy

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Preprint Oct 2026

Improved Explicit and Algorithmic Lower Bounds for r(5,t)

We modify a construction of Brada\v{c} \cite{Bradac26} using a vertex ordering to give, for every prime power $q$, an explicit $K_5$ free graph with more than $q^7$ vertices and independence number below $600q^4$. This shows $$r(5,t)=\Omega(t^{7/4}).$$ Additionally, pruning a graph defined by the Coulter and Matthews p...

Amrit Kandasamy, Lawrence Zhou, Levi Segal · 0 citations

Preprint Oct 2026

Tuza's Conjecture for Graphs of Maximum Degree at Most 10

For a finite simple graph $G$, let $\nu(G)$ be the maximum number of pairwise edge disjoint triangles and $\tau(G)$ the minimum number of edges meeting every triangle. Tuza conjectured in 1981 that every such $G$ satisfies $\tau(G) \le 2 \nu(G).$ We prove the conjecture for the class of graphs with $\Delta\le10.$

Amrit Kandasamy · 0 citations