Forbidden Induced Subgraphs of Double-split Graphs
Forbidden Induced Subgraphs of Double-split Graphs
复制标题
双裂图的禁止诱导子图
DOI：
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发表时间：
2010
影响因子：
0.8
通讯作者：
Ilhee Kim
中科院分区：
文献类型：
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作者：
B. Alexeev;A. Fradkin;Ilhee Kim
在证明强完美图定理的过程中，Chudnovsky、Robertson、Seymour 和 Thomas 证明，每个完美图要么属于五个基本类之一，要么承认多个分解之一。其中四个基本类在导出子图的操作下是封闭的（并且具有已知的禁止子图特征），而由双分裂图组成的第五个基本类则不是封闭的。如果图是双分割图的归纳子图，则该图是双分割图。我们发现了双重图的禁止诱导子图表征；它包含 44 个图表。
In the course of proving the strong perfect graph theorem, Chudnovsky, Robertson, Seymour, and Thomas showed that every perfect graph either belongs to one of five basic classes or admits one of several decompositions. Four of the basic classes are closed under the operation of taking induced subgraphs (and have known forbidden subgraph characterizations), while the fifth one, consisting of double-split graphs, is not. A graph is doubled if it is an induced subgraph of a double-split graph. We find the forbidden induced subgraph characterization of doubled graphs; it contains 44 graphs.