منابع مشابه
On the Chromatic Number of Random Graphs
In this paper we consider the classical Erdős-Rényi model of random graphs Gn,p. We show that for p = p(n) ≤ n−3/4−δ, for any fixed δ > 0, the chromatic number χ(Gn,p) is a.a.s. , +1, or +2, where is the maximum integer satisfying 2( −1) log( −1) ≤ p(n−1).
متن کاملThe locating-chromatic number for Halin graphs
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...
متن کاملThe Chromatic Number of Random Regular Graphs
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.
متن کاملThe game chromatic number of random graphs
Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of G are colored. The game chromatic number χg(G) is the minimum k for which the first player has a winning strategy. In this paper we analyze the asymptotic behavior of ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2008
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2007.11.009