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 کاملInduced subgraphs of graphs with large chromatic number. XI. Orientations
Fix an oriented graph H, and let G be a graph with bounded clique number and very large chromatic number. If we somehow orient its edges, must there be an induced subdigraph isomorphic to H? Kierstead and Rödl [12] raised this question for two specific kinds of digraph H: the three-edge path, with the first and last edges both directed towards the interior; and stars (with many edges directed o...
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...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2018
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.1296.5c7