论文标题
关于随机图的色数的浓度
On the concentration of the chromatic number of random graphs
论文作者
论文摘要
Shamir和Spencer在1980年代证明了二项式随机图G（N，P）的色数以最多长度的间隔集中在最多ω\ sqrt {n}的间隔中，并且在1990年代，Alon表明，长度ω\ sqrt {n}/\ log n}/\ log n的长度间隔为常数pendices for Constant Edder-persies for Constant-Edders for Constant Edders for panders p for convants percors for vonstances for Constant Edders porsiss for p fors p \ in（0. 0）（0）。我们证明了稀疏的情况下的Shamir-Spencer浓度结果的对数改善，在非常密集的情况p = p = p（n）\至1中，色数的浓度令人惊讶。
Shamir and Spencer proved in the 1980s that the chromatic number of the binomial random graph G(n,p) is concentrated in an interval of length at most ω\sqrt{n}, and in the 1990s Alon showed that an interval of length ω\sqrt{n}/\log n suffices for constant edge-probabilities p \in (0,1). We prove a similar logarithmic improvement of the Shamir-Spencer concentration results for the sparse case p=p(n) \to 0, and uncover a surprising concentration `jump' of the chromatic number in the very dense case p=p(n) \to 1.
