Geodesic
A Note on Longest Paths in Circular Arc Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 419-426.

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As observed by Rautenbach and Sereni [SIAM J. Discrete Math. 28 (2014) 335-341] there is a gap in the proof of the theorem of Balister et al. [Combin. Probab. Comput. 13 (2004) 311-317], which states that the intersection of all longest paths in a connected circular arc graph is nonempty. In this paper we close this gap.
Keywords: circular arc graphs, longest paths intersection 
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Joos, Felix. A Note on Longest Paths in Circular Arc Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 419-426. http://geodesic.mathdoc.fr/item/DMGT_2015_35_3_a1/

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[3] J.M. Keil, Finding Hamiltonian circuits in interval graphs, Inform. Process. Lett. 20 (1985) 201-206. doi:10.1016/0020-0190(85)90050-X

[4] D. Rautenbach and J.-S. Sereni, Transversals of longest paths and cycles, SIAM J. Discrete Math. 28 (2014) 335-341. doi:10.1137/130910658

[5] A. Shabbira, C.T. Zamfirescu and T.I. Zamfirescu, Intersecting longest paths and longest cycles: A survey, Electron. J. Graph Theory Appl. 1 (2013) 56-76. doi:10.5614/ejgta.2013.1.1.6