a note on odd facial total-coloring of cacti

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.