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On the Chromatic Number of Random Graphs
, 2007
"... In this paper we consider the classical ErdősRényi 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. ℓ, ℓ+1, or ℓ+2, where ℓ is the maximum integer satisfying 2(ℓ−1) log(ℓ−1) ≤ p(n−1). ..."
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Cited by 19 (2 self)
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In this paper we consider the classical ErdősRényi 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. ℓ, ℓ+1, or ℓ+2, where ℓ is the maximum integer satisfying 2(ℓ−1) log(ℓ−1) ≤ p(n−1).
The game chromatic number of random graphs
, 2007
"... 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 w ..."
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Cited by 2 (1 self)
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for which the first player has a winning strategy. In this study, we analyze the asymptotic behavior of this parameter for a random graph Gn,p. We show that with high probability, the game chromatic number of Gn,p is at least twice its chromatic number but, up to a multiplicative constant, has the same
THE SET CHROMATIC NUMBER OF RANDOM GRAPHS
"... Abstract. In this paper we study the set chromatic number of a random graph G(n, p) for a wide range of p = p(n). We show that the set chromatic number, as a function of p, forms an intriguing zigzag shape. 1. ..."
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Abstract. In this paper we study the set chromatic number of a random graph G(n, p) for a wide range of p = p(n). We show that the set chromatic number, as a function of p, forms an intriguing zigzag shape. 1.
On the Strong Chromatic Number of Random Graphs
, 2008
"... Let G be a graph with n vertices, and let k be an integer dividing n. G is said to be strongly kcolourable if, for every partition of V (G) into disjoint sets V1 ∪···∪Vr, all of size exactly k, there exists a proper vertex kcolouring of G with each colour appearing exactly once in each Vi. In the ..."
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Cited by 1 (0 self)
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of this parameter for the random graph Gn,p. In the dense case when p ≫ n−1/3, we prove that the strong chromatic number is a.s. concentrated on one value ∆+1, where ∆ is the maximum degree of the graph. We also obtain several weaker results for sparse random graphs.
The timproper chromatic number of random graphs
, 2009
"... We consider the timproper chromatic number of the ErdősRényi random graph Gn,p. The timproper chromatic number χ t (G) is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most t. If t = 0, then this is the usua ..."
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Cited by 20 (12 self)
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We consider the timproper chromatic number of the ErdősRényi random graph Gn,p. The timproper chromatic number χ t (G) is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most t. If t = 0
The ttone chromatic number of random graphs
, 2013
"... A proper 2tone kcoloring of a graph is a labeling of the vertices with elements from ( [k] 2 such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2tone chromatic number of a graph G, denoted τ2(G) is the smallest k such that G admits a pro ..."
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proper 2tone k coloring. In this paper, we prove that w.h.p. for p ≥ Cn −1/4 ln 9/4 n, τ2(Gn,p) = (2 + o(1))χ(Gn,p) where χ represents the ordinary chromatic number. For sparse random graphs with p = c/n, c constant, we prove that τ2(Gn,p) = ⌈( √ 8∆+1+5) /2 ⌉ where ∆ represents the maximum degree
unknown title
, 2006
"... On the chromatic number of random graphs with a fixed degree sequence ..."
Results 1  10
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649,417