7 papers
PL standardness of the four-pentachoron census sphere Q
Vance Faber, Michael Murphy
We prove that the four-pentachoron homotopy \(4\)-sphere \(Q\) singled out in the census of Burke, Burton and Spreer is PL homeomorphic to the standard \(4\)-sphere. The key constr…
The singleton hypergraph is extremal for the Isolation Lemma
Vance Faber, David G. Harris
Let be an inclusion-free hypergraph on vertices. A weight assignment is isolating if there is a unique edge whose weight is m…
All-to-all Routing on Kautz Graphs: Regular Routing Beats Shortest Paths
Vance Faber, Noah Streib
We study packet routing in the Kautz digraph K(d,D), where every ordered pair of distinct vertices is connected by a unique shortest directed path. The regular routing introduced i…
Number of edges with shortest cycle k in a Kautz graph
Vance Faber
For the Kautz digraph , let be the number of oriented edges whose shortest directed cycle has length , and define . We giv…
Spanning Factorizations in Vertex-Transitive Digraphs of Degree 2
Vance Faber
We investigate the existence of spanning 1-factorizations in vertex-transitive digraphs of out-degree d. The open question is whether every such digraph admits a spanning 1-factori…
The Trunk of the Restricted Flip Graph of Triangulated S^3
V. Faber, M. Murphy
Let (\mathcal{F}_M(n)) be the restricted flip graph of (n)-vertex triangulations of a closed connected (3)-manifold (M), whose edges are vertex-preserving (2)--(3) and (3)--(2) bis…
Algebraic Constructions for the Digraph Routing Problems
Nyumbu Chishwashwa, Vance Faber, Noah Streib
Efficiency of routing on a regular digraph often involves finding opitmal properties of the graph. For example, the diameter of a digraph is the maximum distance between any two ve…