# On random subgraphs of Kneser and Schrijver graphs

@article{Kupavskii2015OnRS,
title={On random subgraphs of Kneser and Schrijver graphs},
author={Andrey B. Kupavskii},
journal={ArXiv},
year={2015},
volume={abs/1502.00699}
}
• Mathematics, Computer Science
J. Comb. Theory, Ser. B
• 2022
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.
• 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
• 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} • Mathematics Random 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}$$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 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 • Mathematics Forum 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 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.
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
• 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
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
• 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
• 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,
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.
• Computer Science
SODA
• 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.