Some recent results on domination in graphs

Michael D. Plummer
2006 Discussiones Mathematicae Graph Theory  
In this paper, we survey some new results in four areas of domination in graphs, namely: (1) the toughness and matching structure of graphs having domination number 3 and which are "critical" in the sense that if one adds any missing edge, the domination number falls to 2; (2) the matching structure of graphs having domination number 3 and which are "critical" in the sense that if one deletes any vertex, the domination number falls to 2; (3) upper bounds on the domination number of cubic
more » ... and (4) upper bounds on the domination number of graphs embedded in surfaces.
doi:10.7151/dmgt.1338 fatcat:4kpbebu2fff5zkdg7thtinlhhm