The Distinguishing Chromatic Number of Kneser Graphs
نویسندگان
چکیده
منابع مشابه
The 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...
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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...
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The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
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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.
متن کاملOn the b-chromatic number of Kneser graphs
In this note, we prove that for any integer n ≥ 3 the b-chromatic number of the Kneser graph KG(m,n) is greater than or equal to 2 ( ⌊m 2 ⌋
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/3066