## 5 Citations

### A Strengthening of the Erd\H{o}s-Szekeres Theorem

- Mathematics
- 2020

The Erdős-Szekeres Theorem stated in terms of graphs says that any red-blue coloring of the edges of the ordered complete graph $K_{rs+1}$ contains a red copy of the monotone increasing path with $r$…

### Lower Bounds of Size Ramsey Number for Graphs with Small Independence Number

- MathematicsActa Mathematicae Applicatae Sinica, English Series
- 2021

Let r ≥ 3 be an integer such that r − 2 is a prime power and let H be a connected graph on n vertices with average degree at least d and α ( H ) ≤ βn , where 0 < β < 1 is a constant. We prove that…

### Lower Bounds of Size Ramsey Number for Graphs with Small Independence Number

- MathematicsActa Mathematicae Applicatae Sinica, English Series
- 2021

Let r ≥ 3 be an integer such that r − 2 is a prime power and let H be a connected graph on n vertices with average degree at least d and α(H) ≤ βn, where 0 < β < 1 is a constant. We prove that the…

### On edge‐ordered Ramsey numbers

- MathematicsRandom Struct. Algorithms
- 2020

It is proved that for every edge-ordered graph $H$ on $n$ vertices, the authors have $r_{edge}(H;q) \leq 2^{c^qn^{2q-2}\log^q n}$, where $c$ is an absolute constant.

## References

SHOWING 1-10 OF 21 REFERENCES

### An Alternative Proof of the Linearity of the Size-Ramsey Number of Paths

- MathematicsCombinatorics, Probability and Computing
- 2014

This note provides another proof of this fact that actually gives a better bound, namely, $\^{r} $(Pn) < 137n for n sufficiently large.

### The size Ramsey number of a directed path

- MathematicsJ. Comb. Theory, Ser. B
- 2012

### Path Ramsey Number for Random Graphs

- MathematicsCombinatorics, Probability and Computing
- 2015

It is shown that if pn → ∞, w.h.p., whenever G = G(n, p) is 2-edge-coloured there is a monochromatic path of length (2/3 + o(1))n, which is optimal in the sense that 2/3 cannot be replaced by a larger constant.

### On size Ramsey number of paths, trees, and circuits. I

- MathematicsJ. Graph Theory
- 1983

It is demonstrated that random graphs satisfy some interesting Ramsey type properties and are shown to be finite, simple and undirected graphs.

### A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs

- MathematicsEur. J. Comb.
- 1980

### Monochromatic paths in random tournaments

- MathematicsRandom Struct. Algorithms
- 2019

It is proved that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ logn), which implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

### Explicit construction of linear sized tolerant networks

- Mathematics, Computer ScienceDiscret. Math.
- 1988

### The size Ramsey number

- Mathematics
- 1978

Let denote the class of all graphsG which satisfyG→(G1,G2). As a way of measuring minimality for members of, we define thesize Ramsey number ř(G1,G2) by.We then investigate various questions…