Quadrilateral line graphs (Q2785710)

The quadrilateral line graph \(Q(G)\) of a graph \(G\) has the edges of \(G\) as its vertices and two vertices of \(Q(G)\) are adjacent if the corresponding edges in \(G\) are adjacent and lie in a common 4-cycle. The authors provide sufficient conditions for such graphs to be eulerian and hamiltonian. Examining iterations of \(Q(G)\) next, they explain the difficulty of characterizing convergence in terms of forbidden subgraphs by citing a peculiar property of \(Q(K_{3,3})\).