منابع مشابه
Circular chromatic number of Kneser graphs
This paper proves that for any positive integer n, if m is large enough, then the reduced Kneser graph KG2(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 ≥ 2n2(n − 1), then KG(m, n) has its circular chromatic number equal its chromatic number. This provides strong support f...
متن کاملThe Distinguishing Chromatic Number of Kneser Graphs
A labeling f : V (G) → {1, 2, . . . , d} of the vertex set of a graph G is said to be proper d-distinguishing if it is a proper coloring of G and any nontrivial automorphism of G maps at least one vertex to a vertex with a different label. The distinguishing chromatic number of G, denoted by χD(G), is the minimum d such that G has a proper d-distinguishing labeling. Let χ(G) be the chromatic nu...
متن کاملCircular chromatic numbers of some reduced Kneser graphs
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 6= 5, then the circular chromatic number of KG2(m, 2) is equal to m − 2, its ordinary chromatic number.
متن کاملA combinatorial proof for the circular chromatic number of Kneser graphs
Chen [4] confirmed the Johnson-Holroyd-Stahl conjecture that the circular chromatic number of a Kneser graph is equal to its chromatic number. A shorter proof of this result was given by Chang, Liu, and Zhu [3]. Both proofs were based on Fan’s lemma [5] in algebraic topology. In this article we give a further simplified proof of this result. Moreover, by specializing a constructive proof of Fan...
متن کاملOn the chromatic number of q-Kneser graphs
We show that the q-Kneser graph q K2k:k (the graph on the k-subspaces of a 2k-space over G F(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number qk + qk−1 for k = 3 and for k < q log q − q . We obtain detailed results on maximal cocliques for k = 3.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2003
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(03)00032-7