Eulerian Subgraphs in Graphs with Short Cycles

Abstract

P. Paulraja recently showed that if every edge of a graph $G$ lies in a cycle of length at most $5$ and if $G$ has no induced $K_{i,s}$ as a subgraph, then $G$ has a spanning closed trail. We use a weaker hypothesis to obtain a stronger conclusion. We also give a related sufficient condition for the existence of a closed trail in $G$ that contains at least one end of each edge of $G$.