DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory

Article in press


Authors:

N. Matsumoto, Y. Suzuki

Title:

Non-1-planarity of lexicographic products of graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2019-02-05, Revised: 2019-05-21, Accepted: 2019-05-21, https://doi.org/10.7151/dmgt.2231

Abstract:

In this paper, we show the non-$1$-planarity of the lexicographic product of a theta graph and $K_2$. This result completes the proof of the conjecture that a graph $G\circ K_2$ is $1$-planar if and only if $G$ has no edge belonging to two cycles.

Keywords:

1-planar graph, lexicographic product

PDF
Close