## 19 Citations

### Around a conjecture of ErdH{o}s on graph Ramsey numbers

- Mathematics
- 2012

For given graphs G1 and G2 the Ramsey number R(G1,G2), is the smallest positive integer n such that each blue-red edge coloring of the complete graph Kn contains a blue copy of G1 or a red copy of…

### On two problems in graph Ramsey theory

- MathematicsComb.
- 2012

This work improves the upper bound on the existence of a constant c such that, for any graph H on n vertices, rind(H) ≤ 2cnlogn, and moves a step closer to proving this conjecture.

### On the multicolor Ramsey number of a graph with m edges

- MathematicsDiscret. Math.
- 2016

### Recent developments in graph Ramsey theory

- MathematicsSurveys in Combinatorics
- 2015

There has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics.

### Ramsey numbers of sparse digraphs

- Mathematics
- 2021

Burr and Erdős in 1975 conjectured, and Chvátal, Rödl, Szemerédi and Trotter later proved, that the Ramsey number of any bounded degree graph is linear in the number of vertices. In this paper, we…

### Ramsey numbers with prescribed rate of growth

- Mathematics
- 2022

. Let R ( G ) be the two-colour Ramsey number of a graph G . In this note, we prove that for any non-decreasing function n 6 f ( n ) 6 R ( K n ), there exists a sequence of connected graphs ( G n ) n…

### Chromatic number, clique subdivisions, and the conjectures of Hajós and Erdős-Fajtlowicz

- MathematicsComb.
- 2013

The main ingredient in the proof, which might be of independent interest, is an estimate on the order of the largest clique subdivision which one can find in every graph on n vertices with independence number α.

### Ramsey numbers of degenerate graphs

- Mathematics
- 2015

A graph is $d$-degenerate if all its subgraphs have a vertex of degree at most $d$. We prove that there exists a constant $c$ such that for all natural numbers $d$ and $r$, every $d$-degenerate graph…

### Small Ramsey Numbers

- Mathematics, Computer Science
- 2011

We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are…

## References

SHOWING 1-10 OF 24 REFERENCES

### The Ramsey number of a graph with bounded maximum degree

- MathematicsJ. Comb. Theory, Ser. B
- 1983

### On Ramsey Numbers of Sparse Graphs

- MathematicsCombinatorics, Probability and Computing
- 2003

It is shown that, for every , sufficiently large n, and any graph H of order , either H or its complement contains a (d,n)-common graph, that is, a graph in which every set of d vertices has at least n common neighbours.

### Turán Numbers of Bipartite Graphs and Related Ramsey-Type Questions

- MathematicsCombinatorics, Probability and Computing
- 2003

It is proved that, for any fixed bipartite graph H in which all degrees in one colour class are at most r, the Turán number is the maximum possible number of edges in a simple graph on n vertices that contains no copy of H.

### On two problems in graph Ramsey theory

- MathematicsComb.
- 2012

This work improves the upper bound on the existence of a constant c such that, for any graph H on n vertices, rind(H) ≤ 2cnlogn, and moves a step closer to proving this conjecture.

### ON THE MAGNITUDE OF GENERALIZED RAMSEY NUMBERS FOR GRAPHS

- Mathematics
- 1973

If G and H are graphs (which will mean finite, with no loops or parallel lines), define the Ramsey number r(G, H) to be the least number p such that if the lines of the complete graph Kp are colored…

### On graphs with linear Ramsey numbers

- MathematicsJ. Graph Theory
- 2000

In this paper, the use of the regularity lemma is avoided altogether, and it is shown that one can in fact take, for some ®xed c, c
< 2 (log )2 in the general case, and even even 1.

### On Bipartite Graphs with Linear Ramsey Numbers

- MathematicsComb.
- 2001

It is shown that for all and there exists a bipartite graph with n vertices and maximum degree at most whose ramsey number is greater than for some absolute constant c>1.

### Hypergraph Packing and Sparse Bipartite Ramsey Numbers

- MathematicsCombinatorics, Probability and Computing
- 2009

We prove that there exists a constant c such that, for any integer Δ, the Ramsey number of a bipartite graph on n vertices with maximum degree Δ is less than 2cΔn. A probabilistic argument due to…