Jaeger etźal.'s Z 3 -connectivity conjecture can be reduced to a consideration of 5-edge-connected K 1 , 3 -free graphs by Lovász etźal. (2013) and Ma etźal. (2014). Let K 1 , 3 + denote the graph obtained from K 1 , 3 by adding an edge connecting two vertices of degree 1. Denote by K 1 , 3 ź the graph obtained from a K 1 , 3 + by adding an edge to one vertex of degree 1. In this paper, we will prove the following two results.(1) If G is a 2-connected { K 1 , 3 , K 1 , 3 + } -free simple graph, then G is Z 3 -connected if and only if G is ...
