منابع مشابه
Borel chromatic number of closed graphs
We construct, for each countable ordinal ξ, a closed graph with Borel chromatic number two and Baire class ξ chromatic number א0. 2010 Mathematics Subject Classification. Primary: 03E15, Secondary: 54H05
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Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
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It is well-known (Feige and Kilian [24], H̊astad [39]) that approximating the chromatic number within a factor of n1−ε cannot be done in polynomial time for ε > 0, unless coRP = NP. Computing the list-chromatic number is much harder than determining the chromatic number. It is known that the problem of deciding if the list-chromatic number is k, where k ≥ 3, is Πp2-complete [37]. In this paper, ...
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y Abstract We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particular, since a planar graph has acyclic chromatic number at most 5, we conclude that the g...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2016
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm152-11-2015