A note on odd facial total-coloring of cacti

Document Type : Original paper


Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Kosice


A facial total-coloring of a plane graph $G$ is a coloring of the vertices and edges such that no facially adjacent edges, no adjacent vertices, and no edge and its endvertices are assigned the same color. A facial total-coloring of $G$ is odd if for every face $f$ and every color $c$, either no element or an odd number of elements incident with $f$ is colored by $c$. In this note we prove that every cactus forest with an outerplane embedding admits an odd facial total-coloring with at most 16 colors. Moreover, this bound is tight.


Main Subjects

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