论文标题
非双方K-Common图
Non-bipartite k-common graphs
论文作者
论文摘要
如果k_n的k边缘色中H的单色拷贝数渐近地最小化，则图H为k-common。对于每个k，我们构建一个连接的非双方K-Common图。这解决了Jagger，Stovicek和Thomason提出的问题[Combinatorica 16（1996），123-141]。我们还表明，只有H是Sidorenko，并且HH是每个K的k-common，并且HH是每个K的本地k-common，则仅当H是局部的Sidorenko时。
A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.
