The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We study complexity of the problem on hereditary subclasses of subcubic graphs. Each such subclass can be described by means of forbidden induced subgraphs. In case of finitely many forbidden induced subgraphs a necessary condition for polynomial-time solvability of the problem in subcubic graphs (unless $P=NP$) is the exclusion of the graph $S_{i,j,k}$, which is a tree with three leaves of distance $i,j,k$ from the only vertex of degree 3. Whether this condition is also sufficient is an open question, which was previously answered only for $S_{1,k,k}$-free subcubic graphs and $S_{2,2,2}$-free subcubic graphs. Combining various algorithmic techniques, in the present paper we generalize both results and show that the problem can be solved in polynomial time for $S_{2,k,k}$-free subcubic graphs, for any fixed value of k.

在次三次图类中，最大独立集问题已知为NP-hard，即顶点度图最多为3。我们在次三次图的遗传子类上研究问题的复杂性。每个此类子类都可以通过禁止诱导子图来描述。在有限的禁止诱导子图的情况下，亚三次图中问题的多项式时间可解性的必要条件（除非$P=ñP$）是图表的排除项 ${\mathrm{小号}}_{\mathrm{一世}，Ĵ，ķ}$，是一棵有三片叶子的树 $\mathrm{一世}，Ĵ，ķ$ 从度3的唯一顶点开始。此条件是否也足够一个开放的问题，以前仅针对 ${\mathrm{小号}}_{\mathrm{1个}，ķ，ķ}$无亚三次图和 ${\mathrm{小号}}_{2，2，2}$-无立方图。结合各种算法技术，在本文中我们对这两个结果进行了概括，并表明该问题可以在多项式时间内解决${\mathrm{小号}}_{2，ķ，ķ}$对于k的任何固定值，都是无立方的次三次图。