论文标题
随机图中星星饱和数的紧密浓度
Tight concentration of star saturation number in random graphs
论文作者
论文摘要
对于给定的图表$ f $和$ g $，包含最小边缘的最小边数$ f $ - $ g $的免费子图称为$ f $ - 饱和号，并表示为$ \ mathrm {satrm {sat}（g，f）$。对于星$ f = k_ {1，r} $，已知$ \ mathrm {sat}（g（n，p），f）$的渐近学。我们证明了一个更敏锐的结果：WHP $ \ MATHRM {SAT}（g（n，p），k_ {1，r}）$集中在连续2个点集中。
For given graphs $F$ and $G$, the minimum number of edges in an inclusion-maximal $F$-free subgraph of $G$ is called the $F$-saturation number and denoted $\mathrm{sat}(G, F)$. For the star $F=K_{1,r}$, the asymptotics of $\mathrm{sat}(G(n,p),F)$ is known. We prove a sharper result: whp $\mathrm{sat}(G(n,p), K_{1,r})$ is concentrated in a set of 2 consecutive points.
