广义随机二部图的约化

摘要：

设Γ是广义随机二部图，它有两条边R1和Rr，在R1和Rr之间的每对顶点都有边，但在每条边内没有边，其中所有边都随机地用三种颜色P1; P2; P3着色.本文研究了保持Rl和Rr的Γ的约简，并对包含群Aut（Γ）的Sym（Rl）\timesSym（Rr）中的闭置换子群进行了分类.我们的结果依赖于Nesetril-Rodl的组合定理和随机二部图的强有限子模型性质。

英文摘要：

Let Γbe the generalized random bipartite graph that has two sides Rl and Rr with edges for every pair of vertices between R1 and Rr but no edges within each side, where all the edges are randomly colored by three colors P1; P2; P3. In this paper, we investigate the reducts of Γthat preserve Rl and Rr, and classify the closed permutation subgroups in Sym(Rl)\timesSym(Rr) containing the group Aut(Γ). Our results rely on a combinatorial theorem of Nesetril-Rodl and the strong finite submodel property of the random bipartite graph.

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