V. Faber

collaborators

6 papers

math.CO2026

The singleton hypergraph is extremal for the Isolation Lemma

Vance Faber, David G. Harris

Let $H$ be an inclusion-free hypergraph on $n$ vertices. A weight assignment $w : [n] \to [d]$ is isolating if there is a unique edge $e$ whose weight $w (e) = \sum_{i \in e} w (i)$ is m…

math.CO2026

The Trunk of the Restricted Flip Graph of Triangulated S^3

V. Faber, M. Murphy

Let $F_{M} (n)$ 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…

math.CO2026

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…

math.CO2025

Number of edges with shortest cycle k in a Kautz graph

Vance Faber

For the Kautz digraph $K (d, D)$ , let $I ¨ _{k} (d, D)$ be the number of oriented edges whose shortest directed cycle has length $k + 1$ , and define $I^_{k} (d, D) = I ¨ _{k} (d, D) - I ¨ _{k} (d, D - 1)$ . We…

math.CO2025

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…

math.CO2025

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…