论文信息 - Some sufficient conditions for 1-planar graphs to be Class 1

Some sufficient conditions for 1-planar graphs to be Class 1

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. Let G be a 1-planar graph with maximum degree Δ ( G ) . In this paper, it is shown that ? ' ( G ) = Δ ( G ) if (1) Δ ( G ) ? 9 and G contains no adjacent chordal 5-cycles, or (2) Δ ( G ) ? 8 and G contains no adjacent 4-cycles or no 5-cycles.

Wenwen Zhang | Jian-Liang Wu

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