Finding cohesive subgraphs is a fundamental problem for the analysis of graphs. Clique is a classical model of cohesive subgraph, but several alternative definitions have been given in the literature. In this paper we consider the γ-complete graph model, which is based on relaxing the degree constraint of the clique model, that is $G[S]$ is a γ-complete graph, with $\gamma \in (0,1]$, if and only if every vertex of S has degree at least $\gamma (|S|-1)$ in $G[S]$. In this contribution, we investigate the complexity of the problem that asks for the γ-complete subgraph of maximum order (that is, maximum number of vertices). We show that the problem is W[1]-hard for $\frac{1}{2}\le \gamma <1$ when the parameter is order of the subgraph. Moreover, we show that the problem is fixed-parameter tractable when parameterized by the h-index of the input graph, thus solving an open question in the literature.

查找内聚子图是图分析的基本问题。派系是内聚子图的经典模型，但文献中已经给出了几种替代定义。在本文中，我们考虑基于完全派系模型的度约束的γ完全图模型，即$G[\mathrm{小号}]$是一个γ完全图$\gamma \in （0，\mathrm{1个}]$，且仅当S的每个顶点至少具有度$\gamma （|\mathrm{小号}|-\mathrm{1个}）$ 在 $G[\mathrm{小号}]$。在此贡献中，我们调查了要求最大阶数（即最大顶点数）的γ完全子图的问题的复杂性。我们证明问题在于W [1]-$\frac{\mathrm{1个}}{2}\le \gamma <\mathrm{1个}$当参数是子图的顺序时。此外，我们表明，当通过输入图的h索引对参数进行参数化时，该问题是固定参数可处理的，从而解决了文献中的一个悬而未决的问题。