The genus of complete multipartite graphs
Huadong Su, Gaohua Tang · Discrete Mathematics Algorithms and Applications · 2025
An orientable surface [Formula: see text] is said to be of genus [Formula: see text] if it is topologically homeomorphic to a sphere with [Formula: see text] handles. A graph that can be drawn without crossing on a compact surface of genus [Formula: see text], but not on one of genus [Formula: see text], is called a graph of genus [Formula: see text]. In this paper, we determine all complete multipartite graphs whose orientable genus is 0, 1, 2, respectively.