Work

Planar-Toroidal Decomposition of $K_{12}$

Year: 2026

Type: article

Abstract: In 1978, Anderson and White asked whether there is a decomposition of $K_{12}$ into two graphs, one planar and one toroidal. Using theoretical arguments and a computer search of all maximal planar graphs of order 12, we show that no such decomposition exists. We further show that if $G$ is planar of order 12 and $H\subseteq\overline{G}$ is toroidal, then $H$ has at least two fewer edges than $\overline{G}$. A computer search found all 123 unique pairs $\left(G,H\right)$ that make this an equality. 9 pages

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.16100

Authors: Allan Bickle, Russell Campbell

Institutions: Purdue University West Lafayette, University of the Fraser Valley

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414427912

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