Abstract :
A graph is supereulerian if it contains a spanning closed trail. A graph G is collapsible if for every even subset R ⊆ V(G), there is a spanning connected subgraph of G whose set of odd degree vertices is R. The graph K1 is regarded as a trivial collapsible graph. A graph is reduced if it contains no nontrivial collapsible subgraphs. In this paper, we study the independence numbers of reduced graphs. As an application, we also obtain new degree-sum conditions for supereulerian graphs and collapsible graphs.
