Title of article :
Intersecting longest paths and longest cycles: A survey
Author/Authors :
Shabbir, Ayesha Government College University - Abdus Salam School of Mathematical Sciences, Pakistan , Zamfirescu, Carol T. University of Dortmund - Faculty of Mathematics, Germany , Zamfirescu, Tudor I. Roumanian Academy - “Simion Stoilow” Institute of Mathematics, Romania
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.
Keywords :
longest path , longest cycle , planar graph , lattice , torus , M¨obius strip , Klein bottle
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
