A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of G − C contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.
- Claw-free graph
- Hourglass property
- Hamiltonian graph
Li, M., Yuan, L., Jiang, H., Liu, B., & Broersma, H. J. (2013). Tank-ring factors in supereulerian claw-free graphs. Graphs and combinatorics, 29(3), 599-608. https://doi.org/10.1007/s00373-011-1117-z