当前位置: X-MOL 学术Discret. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Planar graphs having no proper 2-immersions in the plane. II
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-06-04 , DOI: 10.1016/j.disc.2021.112481
Vladimir P. Korzhik

A graph drawn on the plane is 2-immersed in the plane if each edge is crossed by at most two other edges. By a proper 2-immersion of a graph we mean a 2-immersion of the graph in the plane such that there is at least one crossing point. We consider the class T of all finite graphs triangulating the plane such that the graphs have no loops and multiple edges, the vertices have degree 5 and 6 only, and the distance between any two 5-valent vertices is at least 4. In this series of papers we construct graphs of the class T having no proper 2-immersions. In the present paper we study those fragments of a 2-immersion of a graph of the class T which contain a 6-valent vertex lying inside a 3-cycle and adjacent to vertices of the 3-cycle.



中文翻译:

平面图在平面中没有适当的 2 浸。二

如果每条边最多与其他两条边交叉,则在平面上绘制的图形是 2 浸入平面中的。图形的适当的2-浸入是指图形在平面中的2-浸入使得至少有一个交叉点。我们考虑类 在所有有限图中对平面进行三角剖分,使得图没有环和多条边,顶点只有度数 5 和 6,并且任意两个 5 价顶点之间的距离至少为 4。 在本系列论文中,我们构造图班级的 没有适当的 2 次浸泡。在本文中,我们研究了类图的 2-浸入式的那些片段 其中包含一个位于 3 环内并与 3 环的顶点相邻的 6 价顶点。

更新日期:2021-06-05
down
wechat
bug