English

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

Data Structures and Algorithms 2021-10-12 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.2110.04606,
  title  = {Linear-time algorithm for vertex 2-coloring without monochromatic triangles on planar graphs},
  author = {Michał Karpiński and Krzysztof Piecuch},
  journal= {arXiv preprint arXiv:2110.04606},
  year   = {2021}
}
R2 v1 2026-06-24T06:45:46.795Z