Supereulerian graphs, independent sets, and degree-sum conditions (Q1377709)

A graph is supereulerian if it contains a spanning closed trail. A graph \(G\) is collapsible if for every even subset \(R\) of \(V(G)\), there is a spanning connected subgraph of \(G\) whose set of odd degree vertices is \(R\). A graph is reduced if it contains no nontrivial collapsible subgraphs. In this paper, the author studies the independence number of reduced graphs. Of particular interest are applications of these results that generalize known conditions involving lower bounds on the degree-sum of nonadjacent vertices that guarantee that a graph is supereulerian.