Tom Kelly

most citedImproving the Caro-Wei bound and applications to Turán stability

1 citations · 1 across the 3 of their papers we have counts for

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math.CO2024

A Short Proof of the Existence of $K_{q}^{r}$ -absorbers

Michelle Delcourt, Tom Kelly, Luke Postle

We codify a short self-contained proof of the existence of $K_{q}^{r}$ -absorbers implicit in Keevash's original proof of the Existence Conjecture. Combining this with the work of the f…

math.CO2024★ 1 cited

Improving the Caro-Wei bound and applications to Turán stability

Tom Kelly, Luke Postle

We prove that if $G$ is a graph and $f (v) \leq 1/ (d (v) + 1/2)$ for each $v \in V (G)$ , then either $G$ has an independent set of size at least $\sum_{v \in V (G)} f (v)$ or $G$ contains…

math.CO2024

Thresholds for $(n, q, 2)$ -Steiner Systems via Refined Absorption

Michelle Delcourt, Tom Kelly, Luke Postle

We prove that if $p \geq n^{- (q - 6) /2}$ , then asymptotically almost surely the binomial random $q$ -uniform hypergraph $G^{(q)} (n, p)$ contains an $(n, q, 2)$ -Steiner system, provided $…

math.CO2024

Clique Decompositions in Random Graphs via Refined Absorption

Michelle Delcourt, Tom Kelly, Luke Postle

We prove that if $p \geq n^{- \frac{1}{3} + β}$ for some $β > 0$ , then asymptotically almost surely the binomial random graph $G (n, p)$ has a $K_{3}$ -packing containing all but at most $n +…

A Short Proof of the Existence of Kqr​-absorbers

Improving the Caro-Wei bound and applications to Turán stability

Thresholds for (n,q,2)-Steiner Systems via Refined Absorption

Clique Decompositions in Random Graphs via Refined Absorption

A Short Proof of the Existence of $K_{q}^{r}$ -absorbers

Thresholds for $(n, q, 2)$ -Steiner Systems via Refined Absorption