In graph theory, a Hamiltonian cycle is a cycle that visits each vertex exactly once. Hamiltonian cycle has a long history, and I have followed some articles.
We can find plenty of examples of Hamiltonian cycles by using google scholar.
- S. Špacapan, A counterexample to prism-hamiltonicity of 3-connected planar graphs[J]. Journal of Combinatorial Theory, Series B, 2021, 146: 364-371.
- Fabrici I, Harant J, Madaras T, et al. Long cycles and spanning subgraphs of locally maximal 1‐planar graphs[J]. Journal of Graph Theory, 2020, 95(1): 125-137.
- Fabrici I, Madaras T, Timková M, et al. Non-hamiltonian graphs in which every edge-contracted subgraph is hamiltonian[J]. Applied Mathematics and Computation, 2021, 392: 125714.
- Georges J P. Non-Hamiltonian bicubic graphs[J]. Journal of Combinatorial Theory, Series B, 1989, 46(1): 121-124. ...
But what I want to ask is：
- Is there a monograph (or review) of Hamiltonian cycles of graphs (or long cycles of graphs)？
I've been looking for a long time, but I haven't seen some in-depth, systematic monographs. I know that there are monographs on graph coloring, matching, dominating set, crossing number, etc., respectively. There are even several books on some subjects, such as graph coloring or dominating set.