Results 1 to 10 of about 61 (53)
The equivariant topology of stable Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Schrijver introduced the stable Kneser graph $SG_{n,k}, n \geq 1, k \geq 0$. This graph is a vertex critical graph with chromatic number $k+2$, its vertices are certain subsets of a set of cardinality $m=2n+k$.
Carsten Schultz
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Symmetries of the stable Kneser graphs
Advances in Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly +3 more sources
Current Protocols, Volume 3, Issue 2, February 2023., 2023 Abstract A particular challenge to the field of neuroscience involves translating findings from 2D in vitro systems to 3D in vivo environments. Standardized cell culture environments that adequately reflect the properties of the central nervous system (CNS) such as the stiffness, protein composition, and microarchitecture in which to study 3D cell–cell
Cian O'Connor +4 more
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Independence Complexes of Stable Kneser Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 For integers $n\geq 1$, $k\geq 0$, the stable Kneser graph $SG_{n,k}$ (also called the Schrijver graph) has as vertex set the stable $n$-subsets of $[2n+k]$ and as edges disjoint pairs of $n$-subsets, where a stable $n$-subset is one that does not contain any $2$-subset of the form $\{i,i+1\}$ or $\{1,2n+k\}$.
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Coloring the Voronoi tessellation of lattices
Journal of the London Mathematical Society, Volume 104, Issue 3, Page 1135-1171, October 2021., 2021 Abstract In this paper we define the chromatic number of a lattice: It is the least number of colors one needs to color the interiors of the cells of the Voronoi tessellation of a lattice so that no two cells sharing a facet are of the same color. We compute the chromatic number of the root lattices, their duals, and of the Leech lattice, we consider ...
Mathieu Dutour Sikirić +3 more
wiley +1 more source
Deformation retracts of neighborhood complexes of stable Kneser graphs [PDF]
Proceedings of the American Mathematical Society, 2013 In 2003, A. Bjorner and M. de Longueville proved that the neighborhood complex of the stable Kneser graph SG_{n,k} is homotopy equivalent to a k-sphere. Further, for n=2 they showed that the neighborhood complex deformation retracts to a subcomplex isomorphic to the associahedron.
Braun, Benjamin, Zeckner, Matthew
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Shifts of the stable Kneser graphs and hom-idempotence
European Journal of Combinatorics, 2017 A graph $G$ is said to be {\em hom-idempotent} if there is a homomorphism from $G^2$ to $G$, and {\em weakly hom-idempotent} if for some $n \geq 1$ there is a homomorphism from $G^{n+1}$ to $G^n$. Larose et al. [{\em Eur. J. Comb. 19:867-881, 1998}] proved that Kneser graphs $\operatorname{KG}(n,k)$ are not weakly hom-idempotent for $n \geq 2k+1$, $k ...
Pablo Daniel Torres +1 more
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Stable sets of maximal size in Kneser-type graphs
European Journal of Combinatorics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benoit Larose, MALVENUTO, Claudia
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A study of the neighborhood complex of $-stable Kneser graphs
Gradus, 2021 In 1978, Alexander Schrijver defined the stable Kneser graphs as a vertex critical subgraphs of the Kneser graphs. In the early 2000s, Günter M. Ziegler generalized Schrijver’s construction and defined the s-stable Kneser graphs. Thereafter Frédéric Meunier determined the chromatic number of the s-stable Kneser graphs for special cases and formulated a
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The automorphism group of the s-stable Kneser graphs
Advances in Applied Mathematics, 2017 For $k,s\geq2$, the $s$-stable Kneser graphs are the graphs with vertex set the $k$-subsets $S$ of $\{1,\ldots,n\}$ such that the circular distance between any two elements in $S$ is at least $s$ and two vertices are adjacent if and only if the corresponding $k$-subset are disjoint.
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