Puja Samanta

The Cycle Rank Threshold: Perfect Matchings and Bipartite Parter Graphs

A graph on \(n\) vertices is called a Parter graph if there exists a nonsingular symmetric matrix, whose nonzero off-diagonal entries correspond exactly to the edges of the graph, such that all of its principal submatrices of order \(n-1\) are singular. Previously, a graph satisfying this condition was said to have pro...