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.

翻译：如果每个非孤立的顶点都有一些颜色, 其周围的颜色似乎不同寻常。 Petru\ v{s}evski 和\v{S}krekovski 于2021年预测, 每个平面图都承认一个奇数 $5 美元 的颜色。 我们确认外部 1 - 平面图和 2 - 线性平面图的推测值, 它们是两个子类的平面图 。