Intersecting longest paths and longest cycles: a survey. (English) Zbl 1306.05121

Shabbir, Ayesha; Zamfirescu, Carol T.; Zamfirescu, Tudor I.

Electron. J. Graph Theory Appl. 1, No. 1, 56-76 (2013).

Summary: 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 dimension, 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.

MSC:

05C38	Paths and cycles
05C35	Extremal problems in graph theory
05-02	Research exposition (monographs, survey articles) pertaining to combinatorics

Keywords:

longest path; logest cycle; planar graph; lattice; torus; Möbius strip; Klein bottle