It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph $H(v,t)$, which contains as vertices all t-element and $(v-t)$-element subsets of $[v]:=\{1,\dots ,v\}$ (where $v>2t$) and an edge between any two vertices when one is a subset of the other. In this paper, for the special case where $t=2$ and v is an odd prime power, we construct such 1-factorizations using perpendicular arrays. We also revisit two known 1-factorizations of $H(2t+1,t)$ – the lexical factorization and modular factorization. Among other results, we give interesting alternative definitions of these 1-factorizations and design an optimal algorithm for computing the lexical factorization.

构造二分式Kne​​ser图的显式1因子分解是一个充满挑战的开放问题 $H（v，Ť）$，其中包含所有t元素和$（v-Ť）$的元素子集 $[v]：=\{\mathrm{1个}，\dots ，v\}$ （哪里 $v>2Ť$）和两个顶点之间的边（当一个顶点是另一个顶点的子集时）。在本文中，对于特殊情况，$Ť=2$和v是一个奇素数功率，我们使用垂直阵列构造这样1-因式分解。我们还回顾了两个已知的1因式分解$H（2Ť+\mathrm{1个}，Ť）$–词汇分解和模块化分解。在其他结果中，我们给出了这些1分解的有趣定义，并设计了一种用于计算词汇分解的最佳算法。