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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ayesha Shabbir
"Abdus Salam" School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore
Electrical & Electronics Engineering

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Intersecting longest paths and longest cycles: A survey Ayesha Shabbir; Carol T. Zamfirescu; Tudor I. Zamfirescu
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 1, No 1 (2013): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2013.1.1.6

Abstract

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.
Co-Authors Carol T. Zamfirescu Tudor I. Zamfirescu