7-Connected graphs are 4-ordered

Add time:08/14/2019    Source:sciencedirect.com

A graph G is k-ordered if for any distinct vertices v1,v2,…,vk∈V(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 7≤f(4)≤40. We prove that in fact f(4)=7.

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