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引用次数: 0
摘要
对于大 n，我们精确地确定了 n 个顶点上的平面图所包含的诱导子图（\(C_4\)和\(C_5\)）的最大数量。我们证明了在\(C_4\)情况下\(K_{2,n-2}\)唯一地达到了这个最大值，并且我们确定了在\(C_5\)情况下达到最大值的图。这扩展了哈基米和施梅切尔的论文以及戈什、居里、扬泽、保洛斯、萨利亚和萨莫拉的论文中的研究，这两篇论文共同渐近地确定了这两个最大值。
Planar Graphs with the Maximum Number of Induced 4-Cycles or 5-Cycles
For large n we determine exactly the maximum numbers of induced \(C_4\) and \(C_5\) subgraphs that a planar graph on n vertices can contain. We show that \(K_{2,n-2}\) uniquely achieves this maximum in the \(C_4\) case, and we identify the graphs which achieve the maximum in the \(C_5\) case. This extends work in a paper by Hakimi and Schmeichel and a paper by Ghosh, Győri, Janzer, Paulos, Salia, and Zamora which together determine both maxima asymptotically.
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