J. Engbers

collaborators

3 papers

math.CO2019

Tomescu's graph coloring conjecture for $ℓ$ -connected graphs

John Engbers, Aysel Erey, Jacob Fox +1

Let $P_{G} (k)$ be the number of proper $k$ -colorings of a finite simple graph $G$ . Tomescu's conjecture, which was recently solved by Fox, He, and Manners, states that $P_G(k) \le k!…

math.CO2019

Colored Multipermutations and a Combinatorial Generalization of Worpitzky's Identity

John Engbers, Jay Pantone, Christopher Stocker

Worpitzky's identity expresses $n^{p}$ in terms of the Eulerian numbers and binomial coefficients: $n^{p} = i = 0 \sum p - 1 i p (p n + i) .$ Pita-Ruiz recent…

math.CO2019

Independent Sets in n-vertex k-chromatic, \ell-connected graphs

John Engbers, Lauren Keough, Taylor Short

We study the problem of maximizing the number of independent sets in $n$ -vertex $k$ -chromatic $ℓ$ -connected graphs. First we consider maximizing the total number of independent…

Tomescu's graph coloring conjecture for ℓ-connected graphs

Colored Multipermutations and a Combinatorial Generalization of Worpitzky's Identity

Independent Sets in n-vertex k-chromatic, \ell-connected graphs

Tomescu's graph coloring conjecture for $ℓ$ -connected graphs