Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 8 3 2023 09 01 A note on odd facial total-coloring of cacti 589 594 14458 10.22049/cco.2022.27895.1388 EN Julius Czap Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Kosice Journal Article 2022 06 22 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. https://comb-opt.azaruniv.ac.ir/article_14458_5845ed2278653c2ca1ef0b462e225152.pdf