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:

B. Niu and X. Zhang

Title:

On $(p,1)$-total labelling of some 1-planar graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-03-16, Revised: 2018-12-14, Accepted: 2019-02-01, https://doi.org/10.7151/dmgt.2208

Abstract:

A graph is $1$-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the $(p,1)$-total labelling number ($p\geq 2$) of every 1-planar graph $G$ is at most $\Delta(G)+2p-2$ provided that $\Delta(G)\geq 6p+7$ or $\Delta(G)\geq 4p+6$ and $G$ is triangle-free.

Keywords:

1-planar graph, total coloring, $ (p, 1)$-total labelling, structural theorem

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