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Algorithms for 1-Planar Graphs
2020A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. This chapter reviews the algorithmic results on 1-planar graphs. We first review a linear time algorithm for testing maximal 1-planarity of a graph if a rotation system (i.e., the circular ...
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Note on improper coloring of $1$-planar graphs
Czechoslovak Mathematical Journal, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chu, Yanan, Sun, Lei, Yue, Jun
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Remarks on the joins of 1-planar graphs
Applied Mathematics and Computation, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhangdong Ouyang, Jun Ge, Yichao Chen
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Incidence Coloring of Outer-1-planar Graphs
Acta Mathematicae Applicatae Sinica, English SeriesA proper incidence $k$-coloring of a graph $G$ is a coloring of the incidences using $k$ colors in such a way that every two adjacent incidences have distinct colors. The minimum integer $k$ such that $G$ has a proper incidence $k$-coloring is the incidence chromatic number of $G$, denoted by $\chi_{i}(G)$.
Qi, Mengke, Zhang, Xin
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