On Dominating Even Subgraphs in Cubic Graphs
Roman Čada, Shuya Chiba, Kenta Ozeki, Kiyoshi Yoshimoto · SIAM Journal on Discrete Mathematics · 2017
It is known that a 3-edge-connected graph has a spanning even subgraph in which every component contains at least five vertices, and the lower bound is best possible. A natural question arises of whether we can improve the lower bound by changing the spanning property with the dominating property. In this paper, we show that a 3-edge-connected cubic graph has a dominating even subgraph in which every component contains at least six vertices.