Coloring outerplanar graphs and planar 3-trees with small monochromatic components
Michael A. Bekos, Carla Binucci, Michael Kaufmann, Chrysanthi, Raftopoulou, Antonios Symvonis, Alessandra Tappini
TL;DR
This paper investigates vertex colorings of certain planar graphs, aiming to minimize the size of monochromatic connected components with two or three colors, providing improved bounds for specific subclasses.
Contribution
It offers new bounds on monochromatic component sizes in outerplanar graphs and planar 3-trees, advancing understanding of graph colorings with small monochromatic components.
Findings
Improved bounds for maximal outerplanar graphs
Enhanced bounds for planar 3-trees
Focus on colorings with two and three colors
Abstract
In this work, we continue the study of vertex colorings of graphs, in which adjacent vertices are allowed to be of the same color as long as each monochromatic connected component is of relatively small cardinality. We focus on colorings with two and three available colors and present improved bounds on the size of the monochromatic connected components for two meaningful subclasses of planar graphs, namely maximal outerplanar graphs and complete planar 3-trees.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Limits and Structures in Graph Theory