Graphs that admit square 1-factorizations are hamiltonian Cayley graphs (Q1906856)

The main result combines three different graph concepts: 1-factorization, hamiltonicity and vertex transitivity. The author has proved the following theorem: Let \(\Gamma\) be a connected graph. \(\Gamma\) has a square 1-factorization if and only if \(\Gamma\) is a Cayley graph on the group \((Z_2)^n\) for some \(n\). From this follows that a connected graph with a square 1-factorization is vertex transitive and hamiltonian. Also it contains an \(n\)-dimensional cube as a spanning subgraph.