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:

O. Zhangdong

Title:

A note on the crossing numbers of 5-regular graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-05-08, Revised: 2019-01-07, Accepted: 2019-01-07, https://doi.org/10.7151/dmgt.2203

Abstract:

The crossing number $\CR(G)$ of a graph $G$ is the smallest number of edge crossings in any drawing of $G$. In this paper, we prove that there exists a unique 5-regular graph $G$ on 10 vertices with $\CR(G)=2$. This answers a question by Chia and Gan in the negative. In addition, we also give a new proof of Chia and Gan's result which states that if $G$ is a non-planar 5-regular graph on 12 vertices, then $\CR(G)\ge 2$.

Keywords:

crossing number, 5-regular graph, drawing

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