This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention. Graphs embeddable in the cubic lattice of arbitrary dimen- sion, and graphs embeddable in the triangular or hexagonal lattice of the plane are also discussed. Results concerning the case when not all, but just some longest paths or cycles are intersected, for example two or three of them, are also reported.
Shabbir, A., Zamfirescu, C. T., & Zamfirescu, T. I. (2013). Intersecting longest paths and longest cycles: A survey. Electronic Journal of Graph Theory and Applications, 1(1), 56–76. https://doi.org/10.5614/ejgta.2013.1.1.6