Jonathan Cutler

collaborators

Showing math.COShow all

3 papers · 1 filter

math.CO2024

A note on the alternating number of independent sets in a graph

Jonathan Cutler, Nathan Kahl, Phoebe Zielonka

The independence polynomial of a graph $G$ evaluated at $- 1$ , denoted here as $I (G; - 1)$ , has arisen in a variety of different areas of mathematics and theoretical physics as an obj…

math.CO2024

Sums, Differences and Dilates

Jonathan Cutler, Luke Pebody, Amites Sarkar

Given a set of integers $A$ and an integer $k$ , write $A + k \cdot A$ for the set ${a + k b : a \in A, b \in A}$ . Hanson and Petridis showed that if $∣ A + A ∣ \leq K ∣ A ∣$ then $|A+2\cdot A|\le K^…

math.CO2024

Nordhaus-Gaddum inequalities for the number of cliques in a graph

Deepak Bal, Jonathan Cutler, Luke Pebody

Nordhaus and Gaddum proved sharp upper and lower bounds on the sum and product of the chromatic number of a graph and its complement. Over the years, similar inequalities have been…