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The Cartographer
Coloring outerplanar graphs and planar 3-trees with small monochromatic components
November 25, 2019 Β· Declared Dead Β· π arXiv.org
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Authors
Michael A. Bekos, Carla Binucci, Michael Kaufmann, Chrysanthi Raftopoulou, Antonios Symvonis, Alessandra Tappini
arXiv ID
1911.10863
Category
cs.DS: Data Structures & Algorithms
Cross-listed
math.CO
Citations
1
Venue
arXiv.org
Last Checked
4 months ago
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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