Independence Complexes of Stable Kneser Graphs
نویسندگان
چکیده
منابع مشابه
Independence Complexes of Stable Kneser Graphs
For integers n ≥ 1, k ≥ 0, the stable Kneser graph SGn,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}. The stable Kneser graphs have been an interesting object of study since the late 1970’s when A. Schrijver de...
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It is well known that the automorphism group of the Kneser graph KGn,k is the symmetric group on n letters. For n ≥ 2k + 1, k ≥ 2, we prove that the automorphism group of the stable Kneser graph SGn,k is the dihedral group of order 2n. Let [n] := [1, 2, 3, . . . , n]. For each n ≥ 2k, n, k ∈ {1, 2, 3, . . .}, the Kneser graph KGn,k has as vertices the k-subsets of [n] with edges defined by disj...
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A graph G is said to be hom-idempotent if there is a homomorphism from G2 to G, and weakly hom-idempotent if for some n ≥ 1 there is a homomorphism from Gn+1 to Gn. Larose et al. (1998) proved that Kneser graphs KG(n, k) are not weakly hom-idempotent for n ≥ 2k + 1, k ≥ 2. For s ≥ 2, we characterize all the shifts (i.e., automorphisms of the graph that map every vertex to one of its neighbors) ...
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We introduce a family of vertex-transitive graphs with specified subgroups of automorphisms which generalise Kneser graphs, powers of complete graphs and Cayley graphs of permutations. We compute the stability ratio for a wide class of these. Under certain conditions we characterise their stable sets of maximal size. © 2003 Elsevier Ltd. All rights reserved. MSC (2000): 05D05; 05C99
متن کاملOn the Chromatic Number of Generalized Stable Kneser Graphs
For each integer triple (n, k, s) such that k ≥ 2, s ≥ 2, and n ≥ ks, define a graph in the following manner. The vertex set consists of all k-subsets S of Zn such that any two elements in S are on circular distance at least s. Two vertices form an edge if and only if they are disjoint. For the special case s = 2, we get Schrijver’s stable Kneser graph. The general construction is due to Meunie...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/605