The totally-perfect bipartite graph and its construction

Abstract

A bipartite graph with vertex sets R and L (|R| ≥ |L|) is called totally-perfect if there is a perfect matching from L, to R for any Ls ⊂ Ls (|Ls| I ≤ |R|). The difference of maximum and minimum degrees of the vertices in L (R) is called the L-skew (R-skew). This paper provides a construction of totally-perfect bipartite graphs with the minimum number of edges add with R-skew being 0 and L-skew 1 or 0. Applications are in the design of direct concentrators of a category and the optimum design of switch architectures of a VLSI chip.