2020/12/27 by Guoli Ding, Chengfu Qin, Ding, Guoli +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.2012.13974
arxiv created 2020/12/27 · arxiv updated 2020/12/29
The chain theorem of Tutte states that every 3-connected graph can be constructed from a wheel Wn by repeatedly adding edges and splitting vertices. It is not difficult to prove the following strengthening of this theorem: every non-wheel 3-connected graph can be constructed from W4 by repeatedly adding edges and splitting vertices. In this paper we similarly strengthen several chain theorems for various versions of 4-connectivity.