5 papers
Hyperoctahedral Eulerian Idempotents, Hodge Decompositions, and Signed Graph Coloring Complexes
Benjamin Braun, Sarah Crown Rundell
Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top…
Asymmetric -colorings of graphs
Erica Flapan, Sarah Rundell, Madeline Wyse
We show that the edges of every 3-connected planar graph except can be colored with two colors in such a way that the graph has no color preserving automorphisms. Also, we ch…
The coloring complex and cyclic coloring complex of a complete k-uniform hypergraph
Sarah Crown Rundell
In this paper, we study the homology of the coloring complex and the cyclic coloring complex of a complete -uniform hypergraph. We show that the coloring complex of a complete $…
The cyclic coloring complex of a complete k-uniform hypergraph
Sarah Crown Rundell
In this paper, we study the homology of the cyclic coloring complex of three different types of -uniform hypergraphs. For the case of a complete -uniform hypergraph, we show…
A Note on the Hodge Structure of the Intersection of Coloring Complexes
Sarah Crown Rundell
Let be a simple graph with vertices. The coloring complex was defined by Steingr\'ımsson, and the homology of was shown to be nonzero only in dimension …