Saturation Numbers for Linear Forests 2 P 4 ∪
Saturation Numbers for Linear Forests 2 P 4 ∪
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DOI：
10.1155/2021/6613393
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发表时间：
2021-05
影响因子：
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通讯作者：
Feifei Song;Yan Zou;Heng-Chuan Su
中科院分区：
文献类型：
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作者：
Feifei Song;Yan Zou;Heng-Chuan Su
在这篇文章中，我们只讨论简单的图形。通常，路和具有n个顶点的完全图分别用Pn和Kn表示。对于本文中没有定义的术语和符号，读者可以参考[1]。对于给定的图F，如果G不包含F的拷贝，但G + e有F的拷贝，其中e <$E（G），则称G是F-饱和的。，e著名的Turán数[2]，记为ex（n，F），是所有大小为n的F-饱和图中图的最大数.作为补充，饱和数sat（n，F）是所有具有n个图的F-饱和图中图的最小尺寸。我们使用SAT（n，F）表示SAT（n，F）中具有最小数大小的图的集合。1964年，Erdans等人在文献[3]中引入了饱和数的概念，并给出了Kt的饱和数。Kászonyi等人在[4]中给出了当F是一类禁止图时sat（n，F）的一般上界.对于更广泛的图F，F的饱和数已经被许多学者研究过，例如k-边连通图[5]、团[6，7]、完全二部图[8，9]、几乎完全图[10]、书籍[11]、圈[12-17]、树[18，19]和森林[20-22]。读者可以在[23]中看到已知结果的总结。在[24]中，Bushmann等人给出了线性森林的Turán数。相应地，Chen等人在[20]中集中研究了饱和数。，ey获得了一组有趣的结果;其中一些结果如以下结果所示。
In this article, we only deal with simple graph. Usually, the path and the complete graph with n vertices are denoted by Pn and Kn, respectively. For terminology and notations not undefined in this paper, the reader can refer to [1]. For a given graph F, graph G is called F-saturated if G does not contain a copy of F, but G + e has a copy of F, where e ∉ E(G). ,e famous Turán number [2], denoted by ex(n, F), is the maximum number size of graphs in all F-saturated graphs with size n. As a complement, saturation number, denoted by sat(n, F), is the minimum size of graphs in all F-saturated graphs with size n. We use SAT (n, F) which denotes the set of graphs with a minimum number size in SAT(n, F). In 1964, Erdős et al. introduced the notion of the saturation number and gave the saturation number of Kt in [3]. Kászonyi et al. gave the general upper bound of sat(n, F) in [4], when F is a kind of forbidden graphs. ,en, for a wider range of graphs F, saturation number of F has been studied by many scholars, for example, k-edge-connected graph [5], cliques [6, 7], complete bipartite graphs [8, 9], nearly complete graphs [10], books [11], cycles [12–17], trees [18, 19], and forests [20–22]. ,e reader can see summary of known results in [23]. In [24], Bushaw et al. gave the Turán number for the linear forest. Corresponding to that, Chen et al. concentrated on the saturation numbers in [20]. ,ey obtained an interesting set of results; some of those are shown as the following results.