Supereulerian graphs, independent sets, and degree-sum conditions

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  K 1  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.