On the length of longest dominating cycles in graphs

Hoa Vu Dinh
1993 Discrete Mathematics  
Vu Dinh, H., On the length of longest dominating cycles in graphs, Discrete Mathematics 121 (1993) 21 l-222. A cycle C in an undirected and simple graph G is dominating if G -C is edgeless. A graph G is called cycle-dominable if G contains a dominating cycle. There exists l-tough graph in which no longest cycle is dominating. Moreover, the difference of the length of a longest cycle and of a longest dominating cycle in a l-tough cycle-dominable graph may be made arbitrarily large. Some lower
more » ... nds for the length of dominating cycles in cycle-dominable graph are given. These results generalize and strengthen some well-known theorems of Jung and Fraisse (1989) and Bauer and Veldman et al. (1988) .
doi:10.1016/0012-365x(93)90554-7 fatcat:wqjo6awccbhbfj7cgmrq7a7ox4