Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-06-04 , DOI: 10.1016/j.tcs.2020.06.003 Kai Jin
It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph , which contains as vertices all t-element and -element subsets of (where ) and an edge between any two vertices when one is a subset of the other. In this paper, for the special case where and v is an odd prime power, we construct such 1-factorizations using perpendicular arrays. We also revisit two known 1-factorizations of – 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.
中文翻译:
关于二分式Kneser图的一阶分解
构造二分式Kneser图的显式1因子分解是一个充满挑战的开放问题 ,其中包含所有t元素和的元素子集 (哪里 )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,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–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。