The size-Ramsey number of 3-uniform tight paths

Han, Jie; Kohayakawa, Yoshiharu; Letzter, Shoham; Mota, Guilherme Oliveira; Parczyk, Olaf

doi:10.19086/aic.24581

Cited by 3 publications

(1 citation statement)

References 16 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Subsequent work has extended this result to many other families of graphs, including bounded-degree trees [15], cycles [21], and, more recently, powers of paths and bounded-degree trees [6] and long subdivisions [12]. For some further recent developments, see [8,19,20,23,26].…”

mentioning

confidence: 99%

The size‐Ramsey number of cubic graphs

Conlon

Nenadov

Trujić

2022

Bulletin of London Math Soc

View full text Add to dashboard Cite

We show that the size-Ramsey number of any cubic graph with n vertices is Opn 8{5 q, improving a bound of n 5{3`op1q due to Kohayakawa, Rödl, Schacht, and Szemerédi. The heart of the argument is to show that there is a constant C such that a random graph with Cn vertices where every edge is chosen independently with probability p ě Cn ´2{5 is with high probability Ramsey for any cubic graph with n vertices. This latter result is best possible up to the constant.

show abstract

mentioning

confidence: 99%

The size‐Ramsey number of cubic graphs

Conlon

Nenadov

Trujić

2022

Bulletin of London Math Soc

View full text Add to dashboard Cite

show abstract

Three Early Problems on Size Ramsey Numbers

2023

View full text Add to dashboard Cite

Partition Universality for Hypergraphs of Bounded Degeneracy and Degree

Allen,

Böttcher,

Cecchelli

2023

Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications

View full text Add to dashboard Cite

We consider the following question. When is the random $k$-uniform hypergraph $\Gamma=G^{(k)}(N,p)$ likely to be $r$-partition universal for $k$-uniform hypergraphs of bounded degree and degeneracy? That is, for which~$p$ can we guarantee asymptotically almost surely that in any $r$-colouring of $E(\Gamma)$ there exists a colour $\chi$ such that in $\Gamma$ there are $\chi$-monochromatic copies of all $k$-uniform hypergraphs of maximum vertex degree $\Delta$, degeneracy at most $D$, and $cN$ vertices for some constant $c=c(D,\Delta)>0$. We show that if $\mu>0$ is fixed, then $p\ge N^{-1/D+\mu}$ suffices for a positive answer if $N$ is large. On the other hand, for $p=o(N^{-1/D})$ we show that $G^{(k)}(N,p)$ is likely not to contain some graphs of maximum degree $\Delta$ and degeneracy $D$ on $cN$ vertices at all. This improves the best upper bounds on the minimum number of edges required for a $k$-uniform hypergraph to be partition universal (even for $k=2$) and also for the size-Ramsey problem for most $k$-uniform hypergraphs of bounded degree and degeneracy.

show abstract

The size-Ramsey number of 3-uniform tight paths

Cited by 3 publications

References 16 publications

The size‐Ramsey number of cubic graphs

The size‐Ramsey number of cubic graphs

Three Early Problems on Size Ramsey Numbers

Partition Universality for Hypergraphs of Bounded Degeneracy and Degree

Contact Info

Product

Resources

About