The 3-colorability of planar graphs without cycles of length 4, 6 and 9

TL;DR

This paper proves that planar graphs lacking cycles of lengths 4, 6, and 9 can be colored with only three colors, expanding understanding of graph colorability under specific cycle restrictions.

Contribution

It establishes the 3-colorability of a new class of planar graphs defined by the absence of certain cycle lengths.

Findings

Planar graphs without cycles of length 4, 6, 9 are 3-colorable.

Provides a proof for a specific class of cycle-restricted planar graphs.

Abstract

In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.