Abstract

Given a simple graph, the maximum independent union of cliques problem is to find a maximum-cardinality subset of vertices such that each connected component of the corresponding induced subgraph is a complete graph. This recently introduced problem allows both cliques and independent sets as feasible solutions and is of significant theoretical and applied interest. This paper establishes the complexity of the problem on several classes of graphs (planar, claw-free, and bipartite graphs), and develops an integer programming formulation and an exact combinatorial branch-and-bound algorithm for solving it. Results of numerical experiments with numerous benchmark instances are also reported.

中文翻译：

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集团问题的最大独立联合：复杂性和精确方法

摘要

给定一个简单的图，团的最大独立并集问题是找到顶点的最大基数子集，以使对应的诱导子图的每个连接的组件都是一个完整的图。最近引入的这个问题允许集团和独立集作为可行的解决方案，并且具有重要的理论和应用价值。本文在几类图（平面图，无爪图和二部图）上建立了问题的复杂性，并开发了整数规划公式和精确的组合分支定界算法来求解该问题。还报告了具有大量基准实例的数值实验结果。