Clique decompositions in random graphs via refined absorption
We prove that if $ p\ge n^{-\frac {1}{3}+\beta} $ for some $\beta> 0$, then asymptotically
almost surely the binomial random graph $ G (n, p) $ has a $ K_3 $-packing containing all …
almost surely the binomial random graph $ G (n, p) $ has a $ K_3 $-packing containing all …
Sunflowers in set systems with small VC-dimension
A family of $ r $ distinct sets $\{A_1,\ldots, A_r\} $ is an $ r $-sunflower if for all $1\leqslant i<
j\leqslant r $ and $1\leqslant i'< j'\leqslant r $, we have $ A_i\cap A_j= A_ {i'}\cap A_ {j'} …
j\leqslant r $ and $1\leqslant i'< j'\leqslant r $, we have $ A_i\cap A_j= A_ {i'}\cap A_ {j'} …
Refined absorption: A new proof of the existence conjecture
M Delcourt, L Postle - arxiv preprint arxiv:2402.17855, 2024 - arxiv.org
The study of combinatorial designs has a rich history spanning nearly two centuries. In a
recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating …
recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating …
Proof of the High Girth Existence Conjecture via Refined Absorption
M Delcourt, L Postle - arxiv preprint arxiv:2402.17856, 2024 - arxiv.org
arxiv:2402.17856v1 [math.CO] 27 Feb 2024 Page 1 arxiv:2402.17856v1 [math.CO] 27 Feb
2024 Proof of the High Girth Existence Conjecture via Refined Absorption Michelle Delcourt …
2024 Proof of the High Girth Existence Conjecture via Refined Absorption Michelle Delcourt …
A Short Proof of the Existence of -absorbers
M Delcourt, T Kelly, L Postle - arxiv preprint arxiv:2412.09710, 2024 - arxiv.org
We provide a new short self-contained proof of the existence of $ K_q^ r $-absorbers.
Combining this with the work of the first and third authors yields a proof of the Existence …
Combining this with the work of the first and third authors yields a proof of the Existence …