On path factors of (3,4)-biregular bigraphs

TL;DR

This paper proves that all simple (3,4)-biregular bigraphs have a specific path factor with degree-three endpoints and provides a polynomial algorithm to construct such a factor.

Contribution

It establishes the existence of a particular path factor in (3,4)-biregular bigraphs and introduces a polynomial-time method to find it.

Findings

Existence of a path factor with degree-three endpoints in all simple (3,4)-biregular bigraphs

Development of a polynomial algorithm for constructing the path factor

Enhanced understanding of structure in biregular bipartite graphs

Abstract

A (3,4)-biregular bigraph G is a bipartite graph where all vertices in one part have degree 3 and all vertices in the other part have degree 4. A path factor of G is a spanning subgraph whose components are nontrivial paths. We prove that a simple (3,4)-biregular bigraph always has a path factor such that the endpoints of each path have degree three. Moreover we suggest a polynomial algorithm for the construction of such a path factor.