Joseph Briggs

activity

20162026

most citedRainbow odd cycles

6 citations · 11 across the 13 of their papers we have counts for

collaborators

16 papers

math.DG2026

A discrete view of Gromov's filling area conjecture

Joseph Briggs, Chris Wells

A compact metric surface $M$ isometrically fills a closed metric curve $C$ if $\partial M = C$ and $d_{M} (x, y) = d_{C} (x, y)$ for every $x, y \in C = \partial M$ ; that is, $M$ does not introduc…

math.CO2025

Degree sequences realizing labelled perfect matchings

Joseph Briggs, Jessica McDonald, Songling Shan

Let $n \in N$ and $d_{1} \geq d_{2} \geq d_{n} \geq 1$ be integers. There is characterization of when $(d_{1}, d_{1}, \dots, d_{n})$ is the degree sequence of a graph containing a perf…

math.CO2022

A Proof of the $(n, k, t)$ -Conjectures

Stacie Baumann, Joseph Briggs

An \emph{ $(n, k, t)$ -graph} is a graph on $n$ vertices in which every set of $k$ vertices contains a clique on $t$ vertices. Turán's Theorem, rephrased in terms of graph complements,…

math.CO2021

Transversals and colorings of simplicial spheres

Joseph Briggs, Michael Gene Dobbins, Seunghun Lee

Motivated from the surrounding property of a point set in $R^{d}$ introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simp…

math.CO2021

Choice Functions

Ron Aharoni, Joseph Briggs

This is a survey paper on rainbow sets (another name for ``choice functions''). The main theme is the distinction between two types of choice functions: those having a large (in th…

math.CO2020★ 2 cited

Fractionally balanced hypergraphs and rainbow KKM theorems

Ron Aharoni, Eli Berger, Joseph Briggs +2

A d-partite hypergraph is called *fractionally balanced* if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex sid…

math.CO2020★ 6 cited

Rainbow odd cycles

Ron Aharoni, Joseph Briggs, Ron Holzman +1

We prove that every family of (not necessarily distinct) odd cycles $O_{1}, \dots, O_{2 ⌈ n /2 ⌉ - 1}$ in the complete graph $K_{n}$ on $n$ vertices has a rainbow odd cycle (that…

math.CO2020

Badges and rainbow matchings

Ron Aharoni, Joseph Briggs, Jinha Kim +1

Drisko proved that $2 n - 1$ matchings of size $n$ in a bipartite graph have a rainbow matching of size $n$ . For general graphs it is conjectured that $2 n$ matchings suffice for this…

math.CO2020

Cooperative conditions for the existence of rainbow matchings

Ron Aharoni, Joseph Briggs, Minho Cho +1

Let $k > 1$ , and let $F$ be a family of $2 n + k - 3$ non-empty sets of edges in a bipartite graph. If the union of every $k$ members of $F$ contains a matching of siz…

math.CO2019★ 1 cited

Rainbow independent sets in certain classes of graphs

Ron Aharoni, Joseph Briggs, Jinha Kim +1

For a given class $C$ of graphs and given integers $m \leq n$ , let $f_{C} (n, m)$ be the minimal number $k$ such that every $k$ independent $n$ -sets in any graph be…

math.CO2019

Choice functions in the intersection of matroids

Joseph Briggs, Minki Kim

We prove a common generalization of two results, one on rainbow fractional matchings and one on rainbow sets in the intersection of two matroids: Given $d = r \lceil k \rceil - r +…

math.CO2019

Restricted online Ramsey numbers of matchings and trees

Joseph Briggs, Christopher Cox

Consider a two-player game between players Builder and Painter. Painter begins the game by picking a coloring of the edges of $K_{n}$ , which is hidden from Builder. In each round, Bu…

math.CO2018

Extremal Collections of $k$ -Uniform Vectors

Joseph Briggs, Wesley Pegden

We show any matrix of rank $r$ over $F_{q}$ can have $\leq (k r) (q - 1)^{k}$ distinct columns of weight $k$ if $k \leq O_{q} (lo g r)$ (up to divisibility issues), a…

math.CO2017

Inverting the Turán Problem

Joseph Briggs, Christopher Cox

Classical questions in extremal graph theory concern the asymptotics of $ex (G, H)$ where $H$ is a fixed family of graphs and $G = G_{n}$ is taken fro…

math.CO2016★ 2 cited

Packing Directed and Hamilton Cycles Online

Michael Anastos, Joseph Briggs

Consider a directed analogue of the random graph process on $n$ vertices, where the $n (n - 1)$ edges are ordered uniformly at random and revealed one at a time. It is known that w.h.…

math.CO2016

Packing Hamilton Cycles Online

Joseph Briggs, Alan Frieze, Michael Krivelevich +2

It is known that w.h.p. the hitting time $τ_{2 σ}$ for the random graph process to have minimum degree $2 σ$ coincides with the hitting time for $σ$ edge disjoint Hamilton cycles. In…