当前位置: X-MOL 学术J. Appl. Ind. 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.)
Efficient Solvability of the Weighted Vertex Coloring Problem for Some Two Hereditary Graph Classes
Journal of Applied and Industrial Mathematics Pub Date : 2021-04-22 , DOI: 10.1134/s1990478921010099
O. O. Razvenskaya , D. S. Malyshev

Abstract

The weighted vertex coloring problem for a given weighted graph is to minimize the number of colors so that for each vertex the number of the colors that are assigned to this vertex is equal to its weight and the assigned sets of vertices are disjoint for any adjacent vertices. For all but four hereditary classes that are defined by two connected \(5 \)-vertex induced prohibitions, the computational complexity is known of the weighted vertex coloring problem with unit weights. For four of the six pairwise intersections of these four classes, the solvability was proved earlier of the weighted vertex coloring problem in time polynomial in the sum of the vertex weights. Here we justify this fact for the remaining two intersections.



中文翻译:

两类遗传图类的加权顶点着色问题的有效可解性

摘要

给定加权图的加权顶点着色问题是最小化颜色数量,以便对于每个顶点,分配给该顶点的颜色数量等于其权重,并且所分配的顶点集对于任何相邻的顶点都是不相交的。对于由两个相连的\(5 \)-顶点引起的禁止定义的所有四个遗传类别,已知单位权重的加权顶点着色问题的计算复杂性。对于这四个类别的六个成对相交中的四个,在时间多项式中加权顶点总和中,加权顶点着色问题的可解性被证明是较早的。在这里,我们为其余两个交叉点证明这一事实。

更新日期:2021-04-22
down
wechat
bug