# An Efficient Algorithm to Test Potentially Bipartiteness of Graphical Degree Sequences

## TL;DR

This paper introduces a customizable, efficient algorithm for testing whether a given graphical degree sequence can be realized as a bipartite graph, balancing accuracy and computational complexity.

## Contribution

It presents a novel deterministic algorithm that can be tuned for polynomial-time execution with minimal error probability on bipartiteness testing.

## Key findings

- Algorithm runs in polynomial time with configurable accuracy
- Low error rate on 'yes' instances for bipartite realization
- Provides a partial answer to Rao's question about bipartite testing

## Abstract

As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in polynomial time, at the expense of possibly producing an erroneous output on some "yes" instances but with very low error rate.