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}
}
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28 Citations
Highly Influential Citations
1
Background Citations
10
Methods Citations
3
Results Citations
2

28 Citations

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On the random version of the Erdős matching conjecture

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

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

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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

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

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

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

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…

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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…

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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.

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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.