Graphs with Eulerian chains

Abstract

An eulerian chain in a graph is a continuous route which traces every edge exactly once. It may be finite or infinite, and may have 0,1 or 2 end vertices. For each kind of eulerian chain, there is a characterization of the graphs which admit such a tracing. This paper derives a uniform characterization of graphs with an eulerian chain, regardless of the kind of chain. Relationships between the edge complements of various kinds of finite subgraphs are also investigated, and hence a sharpened version of the eulerian chain characterization is derived.