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Odd coloring of two subclasses of planar graphs (2205.09317v1)

Published 19 May 2022 in math.CO and cs.DM

Abstract: A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. Petru\v{s}evski and \v{S}krekovski conjectured in 2021 that every planar graph admits an odd $5$-coloring. We confirm this conjecture for outer-1-planar graphs and 2-boundary planar graphs, which are two subclasses of planar graphs.

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