Bryce Frederickson

activity

20182026

collaborators

14 papers

math.CO2026

Generic solutions to symmetric linear equations

Bryce Frederickson, Liana Yepremyan

In 1993, Ruzsa showed that for every $k \geq 2$ , there exists a constant $C$ such that every subset $A \subseteq [N]$ of size at least $C N^{1/ k}$ contains $2 k$ distinct elements $…

math.CO2026

Erdős-Sós via random cyclic orderings

Bryce Frederickson

We present a simplified proof of the Erdős-Sós Conjecture on trees in graphs, which is based on its recent resolution by GPT-6 Astra. At the same time, we also give another proof o…

quant-ph2026

Almost all graphs are vertex-minor universal

Ruben Ascoli, Bryce Frederickson, Sarah Frederickson +2

Answering a question of Claudet, we prove that the uniformly random graph $G \sim G (n, 1/2)$ is $Ω (n)$ -vertex-minor universal with high probability. That is, for some…

math.CO2025

Improved Decomposition Bounds for Partition Polytopes and Odd-Covers

Steffen Borgwardt, Zdeněk Dvořák, Bryce Frederickson +2

The assignments of a set of $m$ items into $n$ clusters of prescribed sizes $k_{1}, \dots, k_{n}$ can be encoded as the vertices of the partition polytope $PP (k_{1}, \dots, k_{n})$ . W…

math.CO2025

Towards Graham's rearrangement conjecture via rainbow paths

Matija Bucić, Bryce Frederickson, Alp Müyesser +2

We study an old question in combinatorial group theory which can be traced back to a conjecture of Graham from 1971. Given a group $Γ$ , and some subset $S \subseteq Γ$ , is it possib…

math.CO2024

Treewidth, Hadwiger Number, and Induced Minors

Rutger Campbell, James Davies, Marc Distel +7

Treewidth and Hadwiger number are two of the most important parameters in structural graph theory. This paper studies graph classes in which large treewidth implies the existence o…

math.CO2024

Regular bipartite decompositions of pseudorandom graphs

Asaf Ferber, Bryce Frederickson, Dingjia Mao +2

In 1972, Kotzig proved that for every even $n$ , the complete graph $K_{n}$ can be decomposed into $⌈ lo g_{2} n ⌉$ edge-disjoint regular bipartite spanning subgraphs, which is b…

math.CO2023

Vector space Ramsey numbers and weakly Sidorenko affine configurations

Bryce Frederickson, Liana Yepremyan

For $B \subseteq F_{q}^{m}$ , the $n$ -th affine extremal number of $B$ is the maximum cardinality of a set $A \subseteq F_{q}^{n}$ with no subset which is affinely isomorphi…

math.CO2023

Circuit decompositions of binary matroids

Bryce Frederickson, Lukas Michel

Given a simple Eulerian binary matroid $M$ , what is the minimum number of disjoint circuits necessary to decompose $M$ ? We prove that $∣ M ∣/ (rank (M) + 1)$ many circ…

math.CO2023

Path Odd-Covers of Graphs

Steffen Borgwardt, Calum Buchanan, Eric Culver +3

We introduce and study "path odd-covers", a weakening of Gallai's path decomposition problem and a strengthening of the linear arboricity problem. The "path odd-cover number" $p_2(…

math.CO2023

Triangle Percolation on the Grid

Igor Araujo, Bryce Frederickson, Robert A. Krueger +5

We consider a geometric percolation process partially motivated by recent work of Hejda and Kala. Specifically, we start with an initial set $X \subseteq Z^{2}$ , and then it…

math.CO2021

A note on the induced Ramsey theorem for spaces

Bryce Frederickson, Vojtech Rödl, Marcelo Sales

The aim of this note is to give a simplified proof of the induced version of the Ramsey theorem for vector spaces first proved by H. J. Prömel.

math.CO2019

Entropy of Tournament Digraphs

David E. Brown, Eric Culver, Bryce Frederickson +2

The Rényi $α$ -entropy $H_{α}$ of complete antisymmetric directed graphs (i.e., tournaments) is explored. We optimize $H_{α}$ when $α = 2$ and $3$ , and find that as $α$ increases $H_{α}$ 's…

math.CO2018

On splitting and splittable families

Samuel Coskey, Bryce Frederickson, Samuel Mathers +1

A set $A$ is said to split a finite set $B$ if exactly half the elements of $B$ (up to rounding) are contained in $A$ . We study the dual notions: (1) splitting family, which is a c…