1-平面图及其子类的染色
发布时间：2018-09-11 09:57
【摘要】：如果图G可以嵌入在平面上,使得每条边最多被交叉1次,则称其为1-可平面图,该平面嵌入称为1-平面图.由于1-平面图G中的交叉点是图G的某两条边交叉产生的,故图G中的每个交叉点c都可以与图G中的四个顶点(即产生c的两条交叉边所关联的四个顶点)所构成的点集建立对应关系,称这个对应关系为θ.对于1-平面图G中任何两个不同的交叉点c_1与c_2(如果存在的话),如果|θ(c_1)∩θ(c_2)|≤1,则称图G是NIC-平面图;如果|θ(c_1)∩θ(c_2)|=0,即θ(c_1)∩θ(c_2)=?,则称图G是IC-平面图.如果图G可以嵌入在平面上,使得其所有顶点都分布在图G的外部面上,并且每条边最多被交叉一次,则称图G为外1-可平面图.满足上述条件的外1-可平面图的平面嵌入称为外1-平面图.现主要介绍关于以上四类图在染色方面的结果.
[Abstract]:If a graph G can be embedded in a plane so that each edge is crossed at most once, then it is called a 1-planar graph, and the plane embedding is called a 1-planar graph. Because the intersection points in 1-planar graph G are generated by the intersection of two edges of graph G. Therefore, each intersection point c in graph G can establish a corresponding relation with the set of points formed by four vertices in graph G (that is, four vertices associated with two cross edges of c), and this corresponding relation is called 胃. For any two different intersections of 1- plane graph G, c _ S _ 1 and C _ S _ 2 (if there is any), if 胃 (c _ 1) class 胃 (c ~ 2) class 胃 (c2) 鈮，
本文编号：2236365
[Abstract]:If a graph G can be embedded in a plane so that each edge is crossed at most once, then it is called a 1-planar graph, and the plane embedding is called a 1-planar graph. Because the intersection points in 1-planar graph G are generated by the intersection of two edges of graph G. Therefore, each intersection point c in graph G can establish a corresponding relation with the set of points formed by four vertices in graph G (that is, four vertices associated with two cross edges of c), and this corresponding relation is called 胃. For any two different intersections of 1- plane graph G, c _ S _ 1 and C _ S _ 2 (if there is any), if 胃 (c _ 1) class 胃 (c ~ 2) class 胃 (c2) 鈮，
本文编号：2236365
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