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7-Connected graphs are 4-ordered
Journal of Combinatorial Theory Series B ( IF 1.4 ) Pub Date : 2019-07-11 , DOI: 10.1016/j.jctb.2019.07.002
Rose McCarty , Yan Wang , Xingxing Yu

A graph G is k-ordered if for any distinct vertices v1,v2,,vkV(G), it has a cycle through v1,v2,,vk in order. Let f(k) denote the minimum integer so that every f(k)-connected graph is k-ordered. The first non-trivial case of determining f(k) is when k=4, where the previously best known bounds are 7f(4)40. We prove that in fact f(4)=7.



中文翻译:

7个连通图为4阶

如果对于任何不同的顶点,则图Gk阶的v1个v2vķVG,它有一个循环 v1个v2vķ为了。让Fķ 表示最小整数,以便每个 Fķ连通图是k阶的。确定的第一个非平凡案例Fķ 那时候 ķ=4,以前最知名的范围是 7F440。我们证明事实F4=7

更新日期:2019-07-11
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