Planar graphs without cycles of length from 4 to 7 are near-bipartite

TL;DR

This paper proves that planar graphs lacking cycles of lengths 4 to 7 can be partitioned into an independent set and a forest, establishing a near-bipartite property for this class.

Contribution

It demonstrates that planar graphs without certain cycle lengths are near-bipartite, expanding understanding of graph colorability and structure.

Findings

Planar graphs without cycles of length 4 to 7 are near-bipartite.

Such graphs can be partitioned into an independent set and a forest.

This class of graphs exhibits specific structural properties.

Abstract

A graph is near-bipartite if its vertex set can be partitioned into an independent set and a set which induces a forest. In this paper, planar graphs without cycles of length from 4 to 7 are shown to be near-bipartite.