Luke Pebody

activity

20142024

collaborators

3 papers

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…

math.NT2023

On Tribonacci Sequences

Luke Pebody

Let a tribonacci sequence be a sequence of integers satisfying $a_{k} = a_{k - 1} + a_{k - 2} + a_{k - 3}$ for all $k \geq 4$ . For any positive integers $k$ and $n$ , denote by $f_{k} (n)$ the number…

math.CO2014

Maximal-clique partitions and the Roller Coaster Conjecture

Jonathan Cutler, Luke Pebody

A graph $G$ is {\em well-covered} if every maximal independent set has the same cardinality $q$ . Let $i_{k} (G)$ denote the number of independent sets of cardinality $k$ in $G$ . Brown…