A Note on Longest Paths in Circular Arc Graphs

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Abstract

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.

[1] P.N. Balister, E. Győri, J. Lehel and R.H. Schelp, Longest paths in circular arc graphs, Combin. Probab. Comput. 13 (2004) 311-317. doi:10.1017/S0963548304006145

[2] T. Gallai, Problem 4, in: Theory of graphs, Proceedings of the Colloquium held at Tihany, Hungary, September, 1966,. P. Erdős and G. Katona Eds., Academic Press, New York-London; Akadmiai Kiad, Budapest (1968).

[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

Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information


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CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.763
Source Normalized Impact per Paper (SNIP) 2018: 0.934

Mathematical Citation Quotient (MCQ) 2017: 0.36

Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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