Viresh Patel

collaborators

4 papers

math.CO2024

Path decompositions of oriented graphs

Viresh Patel, Mehmet Akif Yıldız

We consider the problem of decomposing the edges of a digraph into as few paths as possible. A natural lower bound for the number of paths in any path decomposition of a digraph $D…

math.CO2023

A near-optimal zero-free disk for the Ising model

Viresh Patel, Guus Regts, Ayla Stam

The partition function of the Ising model of a graph $G = (V, E)$ is defined as $Z_{Ising} (G; b) = \sum_{σ : V \to {0, 1}} b^{m (σ)}$ , where $m (σ)$ denotes the number of edges $e=\{u…

math.CO2023

Cycle Partitions in Dense Regular Digraphs and Oriented Graphs

Allan Lo, Viresh Patel, Mehmet Akif Yıldız

A conjecture of Jackson from 1981 states that every $d$ -regular oriented graph on $n$ vertices with $n \leq 4 d + 1$ is Hamiltonian. We prove this conjecture for sufficiently large $n$ …

math.CO2023

Improved bounds for the zeros of the chromatic polynomial via Whitney's Broken Circuit Theorem

Matthew Jenssen, Viresh Patel, Guus Regts

We prove that for any graph $G$ of maximum degree at most $Δ$ , the zeros of its chromatic polynomial $χ_{G} (x)$ (in $C$ ) lie inside the disc of radius $5.94Δ$ centered at $…