Convex p-partitions of bipartite graphs

TL;DR

This paper proves that for any fixed number p, all partitions of a bipartite graph's vertices into p convex sets can be computed efficiently in polynomial time.

Contribution

It introduces a polynomial-time algorithm for partitioning bipartite graphs into convex sets for fixed p, advancing understanding of graph convexity.

Findings

Polynomial-time algorithm for convex p-partitions in bipartite graphs

Feasibility of partitioning into convex sets for fixed p

Enhanced understanding of convex structures in bipartite graphs

Abstract

A set of vertices X of a graph G is convex if it contains all vertices on shortest paths between vertices of X. We prove that for fixed p, all partitions of the vertex set of a bipartite graph into p convex sets can be found in polynomial time.