Compact topological minors in graphs
Compact topological minors in graphs
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图中的紧致拓扑子集
作者：
T. Jiang
设ε是一个真实的数，使得和t是一个正整数.设n是一个充分大的正整数，是t和ε的函数。我们证明了每个至少有n1+ε条边的n-顶点图都包含Kt的一个细分，其中Kt的每条边被细分小于10/ε次。这改进了[A]中的主要结果。Kostochka和Pyber，Combinatorica 8（1988），83-86]，并解决了一个悬而未决的问题。我们也提出一些问题。© 2010 Wiley Periodicals，Inc. J Graph Theory 67：139 - 152，2011
Let ε be a real number such that and t a positive integer. Let n be a sufficiently large positive integer as a function of t and ε. We show that every n‐vertex graph with at least n1+ε edges contains a subdivision of Kt in which each edge of Kt is subdivided less than 10/ε times. This refines the main result in [A. Kostochka and Pyber, Combinatorica 8 (1988), 83–86] and resolves an open question raised there. We also pose some questions. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:139‐152, 2011