Craig Timmons

activity

20132024

most citedFew

T

copies in

H

-saturated graphs

3 citations · 11 across the 28 of their papers we have counts for

collaborators

33 papers

math.CO2024

Chromatic and achromatic numbers of unitary addition Cayley graphs

Keenan Calhoun, Yeşim Demiroğlu Karabulut, Vincent Pigno +1

Let $R$ be a ring. The unitary addition Cayley graph of $R$ , denoted $U (R)$ , is the graph with vertex $R$ , and two distinct vertices $x$ and $y$ are adjacent if and only…

math.CO2024

Hypergraphs of girth 5 and 6 and coding theory

Kathryn Haymaker, Michael Tait, Craig Timmons

In this paper, we study the maximum number of edges in an $N$ -vertex $r$ -uniform hypergraph with girth $g$ where $g \in {5, 6}$ . Writing $ex_{r} (N, C_{< g})$ f…

math.CO2023

Forbidden subgraphs and complete partitions

John Byrne, Michael Tait, Craig Timmons

A graph is called an $(r, k)$ -graph if its vertex set can be partitioned into $r$ parts, each having at most $k$ vertices and there is at least one edge between any two parts. Let $…

math.CO2021

Generalized sum-free sets and cycle saturated regular graphs

David Davini, Craig Timmons

Gerbner, Patkós, Tuza, and Vizer recently initiated the study of $F$ -saturated regular graphs. One of the essential problems in this line of research is determining when such a gra…

math.CO2021

Upper and lower bounds on the size of $B_{k} [g]$ sets

Griffin Johnston, Michael Tait, Craig Timmons

A subset $A$ of the integers is a $B_{k} [g]$ set if the number of multisets from $A$ that sum to any fixed integer is at most $g$ . Let $F_{k, g} (n)$ denote the maximum size of a $B_k[…

math.CO2021

Regular saturated graphs and sum-free sets

Craig Timmons

In a recent paper, Gerbner, Patkós, Tuza and Vizer studied regular $F$ -saturated graphs. One of the essential questions is given $F$ , for which $n$ does a regular $n$ -vertex $F$ -sa…

math.CO2021★ 2 cited

Minimizing the number of complete bipartite graphs in a $K_{s}$ -saturated graph

Beka Ergemlidze, Abhishek Methuku, Michael Tait +1

A graph $G$ is $F$ -saturated if it contains no copy of $F$ as a subgraph but the addition of any new edge to $G$ creates a copy of $F$ . We prove that for $s \geq 3$ and $t \geq 2$ ,…

math.CO2020

Regular Turán numbers of complete bipartite graphs

Michael Tait, Craig Timmons

Let $rex (n, F)$ denote the maximum number of edges in an $n$ -vertex graph that is regular and does not contain $F$ as a subgraph. We give lower bounds on $\mathrm{rex}(n,…

math.CO2019

Triangles in $K_{s}$ -saturated graphs with minimum degree $t$

Benjamin Cole, Albert Curry, David Davini +1

For $n \geq 15$ , we prove that the minimum number of triangles in an $n$ -vertex $K_{4}$ -saturated graph with minimum degree 4 is exactly $2 n - 4$ , and that there is a unique extremal g…

math.CO2018★ 3 cited

Few $T$ copies in $H$ -saturated graphs

Jürgen Kritschgau, Abhishek Methuku, Michael Tait +1

A graph is $F$ -saturated if it is $F$ -free but the addition of any edge creates a copy of $F$ . In this paper we study the quantity $sat (n, H, F)$ which denotes the minimum…

math.CO2018

$C_{2 k}$ -saturated graphs with no short odd cycles

Craig Timmons

The saturation number of a graph $F$ , written $sat (n, F)$ , is the minimum number of edges in an $n$ -vertex $F$ -saturated graph. One of the earliest results on saturation nu…

math.CO2018

The Anti-Ramsey Problem for the Sidon equation

Vladislav Taranchuk, Craig Timmons

For $n \geq k \geq 4$ , let $A R_{X + Y = Z + T}^{k} (n)$ be the maximum number of rainbow solutions to the Sidon equation $X + Y = Z + T$ over all $k$ -colorings $c : [n] \to [k]$ .…

math.CO2018

The Zarankiewicz problem in 3-partite graphs

Michael Tait, Craig Timmons

Let $F$ be a graph, $k \geq 2$ be an integer, and write $ex_{χ \leq k} (n, F)$ for the maximum number of edges in an $n$ -vertex graph that is $k$ -partite and has no subg…

math.CO2017

Turán numbers for Berge-hypergraphs and related extremal problems

Cory Palmer, Michael Tait, Craig Timmons +1

Let $F$ be a graph. We say that a hypergraph $H$ is a {\it Berge}- $F$ if there is a bijection $f : E (F) \to E (H)$ such that $e \subseteq f (e)$ for every $e \in E (F)$ . Note…

math.CO2017★ 2 cited

A note on the number of edges in a Hamiltonian graph with no repeated cycle length

Joey Lee, Craig Timmons

Let $G$ be an $n$ -vertex graph obtained by adding chords to a cycle of length $n$ . Markström asked for the maximum number of edges in $G$ if there are no two cycles in $G$ with the…

math.CO2017★ 2 cited

Triangle-free induced subgraphs of polarity graphs

Jared Loucks, Craig Timmons

Given a finite projective plane $Π$ and a polarity $θ$ of $Π$ , the corresponding polarity graph is the graph whose vertices are the points of $Π$ . Two distinct vertices $p$ and $p'…

math.CO2017

Planar polynomials and an extremal problem of Fischer and Matousek

Robert S. Coulter, Rex W. Matthews, Craig Timmons

Let $G$ be a 3-partite graph with $k$ vertices in each part and suppose that between any two parts, there is no cycle of length four. Fischer and Matouusek asked for the maximum nu…

math.CO2017

Degenerate Turán problems for hereditary properties

Vladimir Nikiforov, Michael Tait, Craig Timmons

Let $H$ be a graph and $t \geq s \geq 2$ be integers. We prove that if $G$ is an $n$ -vertex graph with no copy of $H$ and no induced copy of $K_{s, t}$ , then $λ(G) = O\left(n^{1-1/s}\…

math.CO2016

Induced Turán numbers

Po-Shen Loh, Michael Tait, Craig Timmons +1

The classical Kővári-Sós-Turán theorem states that if $G$ is an $n$ -vertex graph with no copy of $K_{s, t}$ as a subgraph, then the number of edges in $G$ is at most $O (n^{2 - 1/ s})$ .…

math.CO2016

On $r$ -uniform linear hypergraphs with no Berge- $K_{2, t}$

Craig Timmons

Let $F$ be an $r$ -uniform hypergraph and $G$ be a multigraph. The hypergraph $F$ is a Berge- $G$ if there is a bijection $f : E (G) \to E (F)$ s…

math.CO2016

Upper bounds for $B_{h} [g]$ -sets with small $h$

Craig Timmons

For $g \geq 2$ and $h \geq 3$ , we give small improvements on the maximum size of a $B_{h} [g]$ -set contained in the interval ${1, 2, \dots, N}$ . In particular, we show that a $B_3[…

math.CO2016

Independent sets in polarity graphs

Michael Tait, Craig Timmons

Given a projective plane $Σ$ and a polarity $θ$ of $Σ$ , the corresponding polarity graph is the graph whose vertices are the points of $Σ$ , and two distinct points $p_{1}$ and $p_{2}$ …

math.CO2015

A path Turan problem for infinite graphs

Xing Peng, Craig Timmons

Let $G$ be an infinite graph whose vertex set is the set of positive integers, and let $G_{n}$ be the subgraph of $G$ induced by the vertices ${1, 2, \dots, n}$ . An increasing pat…

math.NT2015

A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Thang Pham, Michael Tait, Craig Timmons +1

We prove a Szemerédi-Trotter type theorem and a sum-product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and o…

Chromatic and achromatic numbers of unitary addition Cayley graphs

Hypergraphs of girth 5 and 6 and coding theory

Forbidden subgraphs and complete partitions

Generalized sum-free sets and cycle saturated regular graphs

Upper and lower bounds on the size of Bk​[g] sets

Regular saturated graphs and sum-free sets

Minimizing the number of complete bipartite graphs in a Ks​-saturated graph

Regular Turán numbers of complete bipartite graphs

Triangles in Ks​-saturated graphs with minimum degree t

Few T copies in H-saturated graphs

C2k​-saturated graphs with no short odd cycles

The Anti-Ramsey Problem for the Sidon equation

The Zarankiewicz problem in 3-partite graphs

Turán numbers for Berge-hypergraphs and related extremal problems

A note on the number of edges in a Hamiltonian graph with no repeated cycle length

Triangle-free induced subgraphs of polarity graphs

Planar polynomials and an extremal problem of Fischer and Matousek

Degenerate Turán problems for hereditary properties

Induced Turán numbers

On r-uniform linear hypergraphs with no Berge-K2,t​

Upper bounds for Bh​[g]-sets with small h

Independent sets in polarity graphs

A path Turan problem for infinite graphs

A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Upper and lower bounds on the size of $B_{k} [g]$ sets

Minimizing the number of complete bipartite graphs in a $K_{s}$ -saturated graph

Triangles in $K_{s}$ -saturated graphs with minimum degree $t$

Few $T$ copies in $H$ -saturated graphs

$C_{2 k}$ -saturated graphs with no short odd cycles

On $r$ -uniform linear hypergraphs with no Berge- $K_{2, t}$

Upper bounds for $B_{h} [g]$ -sets with small $h$