在无建筑图中寻找太阳
Finding a sun in building-free graphs
摘要：
最近证明了判定任意图是否包含太阳是NP完全的。我们证明了一个无建筑图是否包含一个太阳可以在O（min $\{m{n^3}, m^{1.5}n^2\}$）的时间内决定，如果一个太阳存在，它可以被发现在相同的时间范围内。无建筑图类包含许多有趣的完美图类，例如Meyniel图，而Meyniel图又包含hhd-free图，i-三角图和奇偶图。此外，还有一些不完美的图是无建筑的。类的建筑免费图推广了几类图，其中一个有效的测试存在的太阳是已知的。我们还提出了一个顶点消除计划的类（建筑，宝石）-免费图。无（建筑，宝石）图类是距离遗传图类的推广，是无（建筑，太阳）图类的一个限制。
英文摘要：
Deciding whether an arbitrary graph contains a sun was recently shown to be NP-complete. We show that whether a building-free graph contains a sun can be decided in O(min$\{m{n^3}, m^{1.5}n^2\}$) time and, if a sun exists, it can be found in the same time bound. The class of building-free graphs contains many interesting classes of perfect graphs such as Meyniel graphs which, in turn, contains classes such as hhd-free graphs, i-triangulated graphs, and parity graphs. Moreover, there are imperfect graphs that are building-free. The class of building-free graphs generalizes several classes of graphs for which an efficient test for the presence of a sun is known. We also present a vertex elimination scheme for the class of (building, gem)-free graphs. The class of (building, gem)-free graphs is a generalization of the class of distance hereditary graphs and a restriction of the class of (building, sun)-free graphs.
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