3 papers
math.CO2026
Zero-sum Inverse Realization and Property~(P) under Join Operations
G. Arunkumar, Anubhab Pahari, Puja Samanta
We introduce zero-sum inverse realization of property (P) of a graph , obtained by imposing an additional condition \( \mathbf{1}^{\top}A^{-1}\mathbf{1}=0, \) on a matrix $A\in…
math.CO2026
The Cycle Rank Threshold: Perfect Matchings and Property (P) in Bipartite Graphs
Puja Samanta
We determine the maximum cycle rank for which property~(P) is equivalent to the existence of a perfect matching in bipartite graphs. It is known that this equivalence holds for bip…
math.CO2026
On the -vertex problem in Bipartite Graphs
G. Arunkumar, Puja Samanta
In a recent work, Sharma and Panda~\cite{sharma} showed that every bipartite graph with a perfect matching has property (P). In this paper, we investigate the converse direction, i…