论文标题
Turán数字用于炸毁树木的边缘
The Turán number for the edge blow-up of trees
论文作者
论文摘要
图$ f $的边缘爆炸是通过将$ f $替换为$ f $的每个边缘获得的图形所获得的图形，而这个集团的新顶点都不同。在本文中，我们关注的是Turán对树木边缘炸毁的问题。 Erdős等。 （1995）和Chen等。 （2003）解决了恒星的问题。 Glebov（2011）解决了路径的问题。 Liu（2013）将上述结果扩展到循环和特殊的树木家族，最低级别的颜色类别（在较小的颜色类别中）（家族中包括恒星的路径和适当细分）。在本文中，我们将刘的结果扩展到所有树木至少两个在较小颜色类中的树木。与刘的结果相结合，除了一种特殊情况外，Turán对树木边缘炸毁的问题得到了完全解决。此外，我们确定$ \ {k_ {1，k}，kk_2，2k_ {1，k-1} \} $的最大边数 - 免费图形和极值图，这是Abbott等人给出的结果的扩展。 （1972）。
The edge blow-up of a graph $F$ is the graph obtained from replacing each edge in $F$ by a clique of the same size where the new vertices of the cliques are all different. In this article, we concern about the Turán problem for the edge blow-up of trees. Erdős et al. (1995) and Chen et al. (2003) solved the problem for stars. The problem for paths was resolved by Glebov (2011). Liu (2013) extended the above results to cycles and a special family of trees with the minimum degree at most two in the smaller color class (paths and proper subdivisions of stars were included in the family). In this article, we extend Liu's result to all the trees with the minimum degree at least two in the smaller color class. Combining with Liu's result, except one particular case, the Turán problem for the edge blow-up of trees is completely resolved. Moreover, we determine the maximum number of edges in the family of $\{K_{1,k}, kK_2, 2K_{1,k-1}\}$-free graphs and the extremal graphs, which is an extension of a result given by Abbott et al. (1972).
