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95
Colorful subgraphs of Kneserlike graphs
"... Combining Ky Fan’s theorem with ideas of Greene and Matouˇsek we prove a generalization of Dol’nikov’s theorem. Using another variant of the BorsukUlam theorem due to Bacon and Tucker, we also prove the presence of all possible completely multicolored tvertex complete bipartite graphs in tcolored ..."
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Cited by 9 (3 self)
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colored tchromatic Kneser graphs and in several of their relatives. In particular, this implies a generalization of a recent result of G. Spencer and The solution of Kneser’s conjecture in 1978 by László Lovász [19] opened up a new area of combinatorics that is usually referred to as the topological method
Symmetries of the stable kneser graphs
 Advances in Applied Mathematics, 45(1):12
"... Abstract. 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 ∈ { ..."
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Cited by 4 (2 self)
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proved in [5], again using the BorsukUlam theorem, that χ(SGn,k) = n − 2k+ 2. Schrijver also proved that the stable Kneser graphs are vertex critical, i.e. the chromatic number of any proper subgraph of SGn,k is strictly less than n − 2k + 2; for this reason, the stable Kneser graphs are also known
Coloring Reduced Kneser Graphs
, 2003
"... The vertex set of a Kneser graph KG(m, n) consists of all nsubsets of the set [m] ={0, 1,...,m − 1}. Two vertices are defined to be adjacent if they are disjoint as subsets. A subset of [m] is called 2stable if 2 ≤a − b  ≤m − 2 for any distinct elements a and b in that subset. The reduced Kneser ..."
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Kneser graph KG2(m, n) is the subgraph of KG(m, n) induced by vertices that are 2stable subsets. We focus our study on the reduced Kneser graphs KG2(2n +2,n). We achieve a complete analysis of its structure. From there, we derive that the circular chromatic number of KG2(2n +2,n) is equal to its
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 nsubsets of [2n + k] and as edges disjoint pairs of nsubsets, where a stable nsubset is one that does not contain any 2subset of the form {i,i + 1} or {1,2n + k}. The stable Kn ..."
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Cited by 5 (1 self)
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For integers n ≥ 1, k ≥ 0, the stable Kneser graph SGn,k (also called the Schrijver graph) has as vertex set the stable nsubsets of [2n + k] and as edges disjoint pairs of nsubsets, where a stable nsubset is one that does not contain any 2subset of the form {i,i + 1} or {1,2n + k}. The stable
The equivariant topology of stable Kneser graphs
"... Abstract. Schrijver introduced the stable Kneser graph SGn,k, n ≥ 1, k ≥ 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. Björner and de Longueville have shown that its box complex is homotopy equivalent to a s ..."
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Cited by 2 (1 self)
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Abstract. Schrijver introduced the stable Kneser graph SGn,k, n ≥ 1, k ≥ 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. Björner and de Longueville have shown that its box complex is homotopy equivalent to a
Circular chromatic number of Kneser graphs
, 2003
"... This paper proves that for any positive integer n, if m is large enough, then the reduced Kneser graph KG 2 (m, n) has its circular chromatic number equal its chromatic number. This answers a question of Lih and Liu [J. Graph Theory, 2002]. For Kneser graphs, we prove that if m 1), then KG(m,n ..."
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Cited by 5 (2 self)
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This paper proves that for any positive integer n, if m is large enough, then the reduced Kneser graph KG 2 (m, n) has its circular chromatic number equal its chromatic number. This answers a question of Lih and Liu [J. Graph Theory, 2002]. For Kneser graphs, we prove that if m 1), then KG
The Circular Extremality of Some Reduced Kneser Graphs
, 2003
"... For m ≥ 2n, the Kneser graph KG(m, n) has the collection of all nsubsets of [m] = {0, 1,..., m − 1} as its vertex set, and two vertices are adjacent if and only if they are disjoint as subsets. A subset of [m] is called 2stable if 2 ≤ u − v  ≤ m − 2 for distinct elements u and v. The reduced K ..."
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Kneser graph KG2(m, n) is the subgraph of KG(m, n) induced by 2stable subsets. We prove that the circular chromatic number of KG2(2n + 2, n) is equal to its chromatic number.
Generalized Kneser coloring theorems with combinatorial proofs
 INVENTIONES MATH
, 2001
"... The Kneser conjecture (1955) was proved by Lovasz (1978) using the BorsukUlam theorem; all subsequent proofs, extensions and generalizations also relied on Algebraic Topology results, namely the BorsukUlam theorem and its extensions. Only in 2000, Matousek provided the rst combinatorial proof of t ..."
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Cited by 32 (3 self)
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of the Kneser conjecture. Here we provide a hypergraph coloring theorem, with a combinatorial proof, which has as special cases the Kneser conjecture as well as its extensions and generalization by (hyper)graph coloring theorems of Dol'nikov, AlonFranklLovasz, Sarkaria, and Kriz. We also give a
Circular chromatic numbers of some reduced Kneser graphs
 J. GRAPH THEORY
, 2001
"... The vertex set of the reduced Kneser graph KG2(m, 2) consists of all pairs {a, b} such that a, b ∈ {1, 2,..., m} and 2 ≤ a−b  ≤ m−2. Two vertices are defined to be adjacent if they are disjoint. We prove that, if m ≥ 4 and m � = 5, then the circular chromatic number of KG2(m, 2) is equal to m − 2 ..."
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Cited by 4 (0 self)
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The vertex set of the reduced Kneser graph KG2(m, 2) consists of all pairs {a, b} such that a, b ∈ {1, 2,..., m} and 2 ≤ a−b  ≤ m−2. Two vertices are defined to be adjacent if they are disjoint. We prove that, if m ≥ 4 and m � = 5, then the circular chromatic number of KG2(m, 2) is equal to m
Results 1  10
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95