3 papers
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 evaluated at , denoted here as , 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 and an integer , write for the set . Hanson and Petridis showed that if 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…