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摘要
Jaeger et al.'s Z(3)-connectivity conjecture can be reduced to a consideration of 5-edge-connected K-1,K-3-free graphs by Lovasz et al. (2013) and Ma et al. (2014). Let K-1,3(+) denote the graph obtained from K-1,K-3 by adding an edge connecting two vertices of degree 1. Denote by K-1,K-3* 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,K-3, K-1,3(+)}-free simple graph, then G is Z(3)-connected if and only if G is not one of K4,K-4(-) or an n-cycle, where n >= 3. @@@ (2) If G is a 2-connected {K-1,K-3, K-1,K-3*}-free simple graph, then G is not Z(3)-connected if and only if G is isomorphic to one of the 20 specified graphs or G is an n-cycle, where n >= 3.
- 出版日期2016-9-6
- 单位华中师范大学
