Halin图及其推广的简单认识
Simple Recognition of Halin Graphs and Their Generalizations
摘要：
我们描述并实现了两个局部约简规则，可用于识别线性时间的Halin图，避免了以前的线性时间Halin图识别算法的复杂的平面性测试步骤。同样的两个规则可以用作线性时间算法的基础，用于解决Halin图上的其他算法问题，包括将这些图分解为树和圈，找到Hamilton圈或构造平面嵌入。这些约简规则也可以用于识别更广泛的多面体图。这些图，我们称之为D3-可约图，是通过在它们的三角面上将金字塔粘合在一起而形成的多面体的对偶图;它们的树宽是有界的，并且它们必然具有Lombardi图。
英文摘要：
We describe and implement two local reduction rules that can be used to recognize Halin graphs in linear time, avoiding the complicated planarity testing step of previous linear time Halin graph recognition algorithms. The same two rules can be used as the basis for linear-time algorithms for other algorithmic problems on Halin graphs, including decomposing these graphs into a tree and a cycle, finding a Hamiltonian cycle, or constructing a planar embedding. These reduction rules can also be used to recognize a broader class of polyhedral graphs. These graphs, which we call the D3-reducible graphs, are the dual graphs of the polyhedra formed by gluing pyramids together on their triangular faces; their treewidth is bounded, and they necessarily have Lombardi drawings.
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