Linear-time algorithm for vertex 2-coloring without monochromatic triangles on planar graphs

TL;DR

This paper presents a linear-time algorithm for 2-coloring planar graphs to avoid monochromatic triangles, addressing an open problem in graph coloring complexity.

Contribution

The paper provides the first linear-time algorithm for triangle-tree 2-coloring specifically on planar graphs, solving a previously open question.

Findings

Algorithm runs in linear time on planar graphs

Successfully avoids monochromatic triangles in 2-coloring

Addresses an open problem in graph coloring complexity

Abstract

In the problem of 2-coloring without monochromatic triangles (or triangle-tree 2-coloring), vertices of the simple, connected, undirected graph are colored with either 'black' or 'white' such that there are no 3 mutually adjacent vertices of the same color. In this paper we are positively answering the question posed in our previous work, namely, if there exists an algorithm solving 2-coloring without monochromatic triangles on planar graphs with linear-time complexity.