Non-1-Planarity of Lexicographic Products of Graphs

Discussiones Mathematicae Graph Theory

Matsumoto Naoki¹  Suzuki Yusuke² 

[1] Department of Computer and Information Science, Faculty of Science and Technology, Seikei University, Tokyo, Japan;Department of Mathematics, Niigata University8050 Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japan;

关键词: 1-planar graph;    lexicographic product;    05c10;   

DOI  :  10.7151/dmgt.2231

来源: DOAJ

【 摘 要 】

In this paper, we show the non-1-planarity of the lexicographic product of a theta graph and K2. This result completes the proof of the conjecture that a graph G ◦ K2 is 1-planar if and only if G has no edge belonging to two cycles.

【 授权许可】

Unknown