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This paper investigates equitable coloring in planar and outerplanar graphs, establishing necessary and sufficient conditions for equitable s-coloring based on independent set sizes. The authors demonstrate that while the condition holds for outerplanar graphs when s ≥ 6, it fails for s = 3, with the cases for s = 4 and 5 remaining unresolved. Additionally, they present a Planar Theorem that provides a similar result for planar graphs under specific conditions related to vertex degrees and independent sets.

Author

S Micheal Monica

Language

EN