Square of Planar Graphs of Max Degree Four without Five Cycles

TL;DR

This paper proves that the square of certain planar graphs with maximum degree four and no five cycles can be colored with at most 12 colors, advancing understanding of graph coloring constraints.

Contribution

It establishes a new upper bound on the choosability of the square of specific planar graphs, focusing on those without five cycles.

Findings

Choosability of the square is at most 12 for the specified graphs.

The result applies to planar graphs with max degree 4 and no five cycles.

Provides insights into coloring properties of restricted planar graphs.

Abstract

We show that the choosability of the square of planar graphs of max degree 4 without five cycles is at most 12. Keywords: planar graph, choosability AMS Mathematics Subject Classification: 05C15