## 28 Citations

### Sharp bounds for the chromatic number of random Kneser graphs

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. B
- 2022

### Random Kneser graphs and hypergraphs

- MathematicsElectron. J. Comb.
- 2018

A purely combinatorial approach to the problem based on blow-ups of graphs, which gives much better bounds on the chromatic number of random Kneser and Schrijver graphs and Knesers hypergraphs.

### Chromatic number of random Kneser hypergraphs

- MathematicsJ. Comb. Theory, Ser. A
- 2018

### On the random version of the Erd\H{o}s matching conjecture

- Mathematics
- 2018

The Kneser hypergraph ${\rm KG}^r_{n,k}$ is an $r$-uniform hypergraph with vertex set consisting of all $k$-subsets of $\{1,\ldots,n\}$ and any collection of $r$ vertices forms an edge if their…

### Expected Chromatic Number of Random Subgraphs

- Mathematics
- 2018

Given a graph $G$ and $p \in [0,1]$, let $G_p$ denote the random subgraph of $G$ obtained by keeping each edge independently with probability $p$. Alon, Krivelevich, and Sudokov proved $\mathbb{E}…

### Sharp threshold for the Erdős–Ko–Rado theorem

- MathematicsRandom Struct. Algorithms
- 2023

For positive integers n$$ n $$ and k$$ k $$ with n≥2k+1$$ n\ge 2k+1 $$ , the Kneser graph K(n,k)$$ K\left(n,k\right) $$ is the graph with vertex set consisting of all k$$ k $$ ‐sets of {1,…,n}$$…

### On the chromatic number of random subgraphs of a certain distance graph

- MathematicsDiscret. Appl. Math.
- 2019

### On Threshold Probability for the Stability of Independent Sets in Distance Graphs

- MathematicsMathematical Notes
- 2019

This paper considers the so-called distance graph G(n, r, s);its vertices can be identified with the r-element subsets of the set {1, 2,…,n}, and two vertices are joined by an edge if the size of the…

### On Threshold Probability for the Stability of Independent Sets in Distance Graphs

- MathematicsMathematical Notes
- 2019

This paper considers the so-called distance graph G(n, r, s);its vertices can be identified with the r-element subsets of the set {1, 2,…,n}, and two vertices are joined by an edge if the size of the…

## References

SHOWING 1-10 OF 20 REFERENCES

### TRANSFERENCE FOR THE ERDŐS–KO–RADO THEOREM

- MathematicsForum of Mathematics, Sigma
- 2015

For natural numbers $n,r\in \mathbb{N}$ with $n\geqslant r$, the Kneser graph $K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\ldots ,n\}$ in which two sets are adjacent if and…

### A New Short Proof of Kneser's Conjecture

- MathematicsAm. Math. Mon.
- 2002

A very short proof of Kneser's conjecture is produced by combining the celebrated result of Lusterik, Schnirelman, and Borsuk on sphere covers with Gale's theorem concerning the even distribution of points on the sphere that does not rely on Gale's result.

### Kneser's Conjecture

- Mathematics
- 2002

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up in the same class. Lovasz…

### Independence numbers and chromatic numbers of the random subgraphs of some distance graphs

- Mathematics
- 2015

This work is concerned with the Nelson-Hadwiger classical problem of finding the chromatic numbers of distance graphs in . Most consideration is given to the class of graphs defined as follows: where…

### Vertex-critical subgraphs of Kneser-graphs

- Mathematics
- 1978

We show that if the stable (independent) n-subsets of a circuit wit 2n+k vertices are split into k+1 classes, one of the classes contains two disjoint n-subsets; this yields a (k+2)-vertex-critical…

### On the stability of the Erd\H{o}s-Ko-Rado theorem

- Mathematics
- 2014

Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independence number of the…

### Extremal Results in Random Graphs

- Mathematics
- 2013

According to Paul Erdős au][Some notes on Turan’s mathematical work, J. Approx. Theory 29 (1980), page 4]_it was Paul Turan who “created the area of extremal problems in graph theory”. However,…

### On the chromatic number of Kneser hypergraphs

- Mathematics
- 2002

We give a simple and elementary proof of Křiž's lower bound on the chromatic number of the Kneser r-hypergraph of a set system S.

### The Probabilistic Method

- Computer ScienceSODA
- 1992

A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.