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4 papers · 1 filter
Tomescu's graph coloring conjecture for -connected graphs
John Engbers, Aysel Erey, Jacob Fox +1
Let be the number of proper -colorings of a finite simple graph . Tomescu's conjecture, which was recently solved by Fox, He, and Manners, states that $P_G(k) \le k!…
Colored Multipermutations and a Combinatorial Generalization of Worpitzky's Identity
John Engbers, Jay Pantone, Christopher Stocker
Worpitzky's identity expresses in terms of the Eulerian numbers and binomial coefficients: Pita-Ruiz recent…
Reversible peg solitaire on graphs
John Engbers, Christopher Stocker
The game of peg solitaire on graphs was introduced by Beeler and Hoilman in 2011. In this game, pegs are initially placed on all but one vertex of a graph . If forms a pat…
Counting independent sets of a fixed size in graphs with a given minimum degree
John Engbers, David Galvin
Galvin showed that for all fixed and sufficiently large , the -vertex graph with minimum degree that admits the most independent sets is the complete bipartite graph…