Emergent Mind
Odd coloring of two subclasses of planar graphs
(2205.09317)
Published May 19, 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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