论文标题
关于司额分离器和扩展的注释
A note on sublinear separators and expansion
论文作者
论文摘要
对于遗传图表的C类C，让S_C（N）成为最小函数，以使C中的每个N-Vertex图在S_C（N）中具有平衡的顺序分离器，而Nabla_c（r）是C的最小函数，即C的扩展，即在NešetmedThemention thementionnešetmedThemention themistednešetmedThemention理论中的扩展。 Plotkin，Rao和Smith（1994）和Esperet和Raymond（2018）的结果暗示，如果S_C（n）= Theta（N^{1- Epsilon}），对于某些Epsilon> 0，则Nabla_c（r）= Omega（R） nabla_c（r）= o（r^{1/epsilon-1} polylog r）。回答一个埃斯特雷特和雷蒙德的问题，我们表明两个指数都无法显着改善。
For a hereditary class C of graphs, let s_C(n) be the minimum function such that each n-vertex graph in C has a balanced separator of order at most s_C(n), and let nabla_C(r) be the minimum function bounding the expansion of C, in the sense of bounded expansion theory of Nešetřil and Ossona de Mendez. The results of Plotkin, Rao, and Smith (1994) and Esperet and Raymond (2018) imply that if s_C(n)=Theta(n^{1-epsilon}) for some epsilon>0, then nabla_C(r)=Omega(r^{1/(2.epsilon)-1}/polylog r) and nabla_C(r)=O(r^{1/epsilon-1}polylog r). Answering a question of Esperet and Raymond, we show that neither of the exponents can be substantially improved.
