广义Caterpillar图的极大独立集
Maximal Independent Sets in Generalised Caterpillar Graphs
摘要：
毛毛虫图是一棵树，当去掉它所有的悬挂顶点时，它留下一条无弦的路，这条无弦的路称为图的主干。从主干到悬垂顶点的边称为毛毛虫图的头发。Ortiz和Villanueva（C.Ortiz和M.Villanueva，Discrete Applied Mathematics，160（3）：259-266，2012）描述了一种算法，其在输出的大小上是线性的，用于在毛毛虫图中找到一族最大独立集。在本文中，我们提出了一个算法，再次线性的输出大小，为广义毛虫图，在每个顶点的骨干，可以有任何数量的头发的长度为1，最多一个头发的长度为2。
英文摘要：
A caterpillar graph is a tree which on removal of all its pendant vertices leaves a chordless path. The chordless path is called the backbone of the graph. The edges from the backbone to the pendant vertices are called the hairs of the caterpillar graph. Ortiz and Villanueva (C.Ortiz and M.Villanueva, Discrete Applied Mathematics, 160(3): 259-266, 2012) describe an algorithm, linear in the size of the output, for finding a family of maximal independent sets in a caterpillar graph. In this paper, we propose an algorithm, again linear in the output size, for a generalised caterpillar graph, where at each vertex of the backbone, there can be any number of hairs of length one and at most one hair of length two.
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