论文标题
对具有相等独立性和歼灭数字的图表的表征的反面样本
Counterexamples to the characterisation of graphs with equal independence and annihilation number
论文作者
论文摘要
我们反驳了Larson and Pepper（2011）的独立性和歼灭数量的图表的表征。提供了一系列具有任意顶点，任意数量的组件，任意较大的独立性数量和任意大差异的反样本。此外，我们指出了定理证明中的错误。但是，我们表明该定理仍然可用于两部分图和连接的无爪图。
We disprove the characterisation of graphs with equal independence and annihilation number by Larson and Pepper (2011). Series of counterexamples with arbitrary number of vertices, arbitrary number of components, arbitrary large independence number and arbitrary large difference between the critical and the regular independence number are provided. Furthermore, we point out the error in the proof of the theorem. However, we show that the theorem still holds for bipartite graphs and connected claw-free graphs.
