论文标题
1平面图的最大匹配可扩展性和因子临界性
The maximum matching extendability and factor-criticality of 1-planar graphs
论文作者
论文摘要
如果可以在飞机上绘制$ 1 $ - $平面$，则每个边缘在最多的边缘都越过。此外，如果满足$ | e（g）| = 4 | v（g）| -8 $，则1平面图$ g $是$ optimal $。 J. Fujisawa等。 [16]首先考虑了最佳1平面图的匹配扩展，即获得的每个最佳1平面均值图是1-延伸且表征的2-伸展2-伸展最佳的最佳1平面图和3个匹配，也可以扩展到完美匹配。在这篇简短的论文中，我们证明没有最佳$ 1 $ - 平面图是3个扩展的。此外，我们主要获得的是，没有1个平面图是通过排放方法5延伸的，并且还构建了4个伸缩性的1平面图。最后，我们发现没有1个平面图是7因子至关重要的，并且没有最佳的1 planar图是6因子至关重要的。
A graph is $1$-$planar$ if it can be drawn in the plane so that each edge is crossed by at most one other edge. Moreover, a 1-planar graph $G$ is $optimal$ if it satisfies $|E(G)|=4|V(G)|-8$. J. Fujisawa et al. [16] first considered matching extension of optimal 1-planar graphs, obtained that each optimal 1-planar graph of even order is 1-extendable and characterized 2-extendable optimal 1-planar graphs and 3-matchings extendable to perfect matchings as well. In this short paper, we prove that no optimal $1$-planar graph is 3-extendable. Further we mainly obtain that no 1-planar graph is 5-extendable by the discharge method and also construct a 4-extendable 1-planar graph. Finally we get that no 1-planar graph is 7-factor-critical and no optimal 1-planar graph is 6-factor-critical.
