Grace McCourt

activity

20202023

most citedLinear Bounds for Cycle-free Saturation Games

2 citations · 3 across the 8 of their papers we have counts for

collaborators

10 papers

math.CO2023

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs, II: Large uniformities

Alexandr Kostochka, Ruth Luo, Grace McCourt

Dirac proved that each $n$ -vertex $2$ -connected graph with minimum degree $k$ contains a cycle of length at least $min {2 k, n}$ . We obtain analogous results for Berge cycles in h…

math.CO2022

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs

Alexandr Kostochka, Ruth Luo, Grace McCourt

Dirac proved that each $n$ -vertex $2$ -connected graph with minimum degree at least $k$ contains a cycle of length at least $min {2 k, n}$ . We consider a hypergraph version of this…

math.CO2022

On a property of $2$ -connected graphs and Dirac's Theorem

Alexandr Kostochka, Ruth Luo, Grace McCourt

We refine a property of $2$ -connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that eac…

math.CO2022

Minimum degree ensuring that a hypergraph is hamiltonian-connected

Alexandr Kostochka, Ruth Luo, Grace McCourt

A hypergraph $H$ is hamiltonian-connected if for any distinct vertices $x$ and $y$ , $H$ contains a hamiltonian Berge path from $x$ to $y$ . We find for all $3 \leq r < n$ , exact lower…

math.CO2022★ 1 cited

Ramsey-Turán Problems with small independence numbers

József Balogh, Ce Chen, Grace McCourt +1

Given a graph $H$ and a function $f (n)$ , the Ramsey-Turán number $R T (n, H, f (n))$ is the maximum number of edges in an $n$ -vertex $H$ -free graph with independence number at most $f(n…

math.CO2021

Dirac's Theorem for hamiltonian Berge cycles in uniform hypergraphs

Alexandr Kostochka, Ruth Luo, Grace McCourt

The famous Dirac's Theorem gives an exact bound on the minimum degree of an $n$ -vertex graph guaranteeing the existence of a hamiltonian cycle. We prove exact bounds of similar typ…

math.CO2021★ 2 cited

Linear Bounds for Cycle-free Saturation Games

Sean English, Tomáš Masařík, Grace McCourt +3

Given a family of graphs $F$ , we define the $F$ -saturation game as follows. Two players alternate adding edges to an initially empty graph on $n$ vertices, with…

math.CO2021

Low Diameter Monochromatic Covers of Complete Multipartite Graphs

Sean English, Connor Mattes, Grace McCourt +1

Let the diameter cover number, $D_{r}^{t} (G)$ , denote the least integer $d$ such that under any $r$ -coloring of the edges of the graph $G$ , there exists a collection of $t$ monochromat…

math.CO2021

On sizes of 1-cross intersecting set pair systems

Alexandr V. Kostochka, Grace McCourt, Mina Nahvi

Let ${(A_{i}, B_{i})}_{i = 1}^{m}$ be a set pair system. Füredi, Gyárfás and Király called it {\em $1$ -cross intersecting} if $∣ A_{i} \cap B_{j} ∣$ is $1$ when $i \neq = j$ and $0$ if $i = j$ . They…

math.CO2020

Generalizations and strengthenings of Ryser's conjecture

Louis DeBiasio, Yigal Kamel, Grace McCourt +1

Ryser's conjecture says that for every $r$ -partite hypergraph $H$ with matching number $ν (H)$ , the vertex cover number is at most $(r - 1) ν (H)$ . This far reaching generalization of K…

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs, II: Large uniformities

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs

On a property of 2-connected graphs and Dirac's Theorem

Minimum degree ensuring that a hypergraph is hamiltonian-connected

Ramsey-Turán Problems with small independence numbers

Dirac's Theorem for hamiltonian Berge cycles in uniform hypergraphs

Linear Bounds for Cycle-free Saturation Games

Low Diameter Monochromatic Covers of Complete Multipartite Graphs

On sizes of 1-cross intersecting set pair systems

Generalizations and strengthenings of Ryser's conjecture

On a property of $2$ -connected graphs and Dirac's Theorem