A Note on Longest Paths in Circular Arc Graphs

Felix Joos

Discussiones Mathematicae Graph Theory (2015)

  • Volume: 35, Issue: 3, page 419-426
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Felix Joos. "A Note on Longest Paths in Circular Arc Graphs." Discussiones Mathematicae Graph Theory 35.3 (2015): 419-426. <http://eudml.org/doc/271225>.

@article{FelixJoos2015,
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.},
author = {Felix Joos},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {circular arc graphs; longest paths intersection},
language = {eng},
number = {3},
pages = {419-426},
title = {A Note on Longest Paths in Circular Arc Graphs},
url = {http://eudml.org/doc/271225},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Felix Joos
TI - A Note on Longest Paths in Circular Arc Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 3
SP - 419
EP - 426
AB - 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.
LA - eng
KW - circular arc graphs; longest paths intersection
UR - http://eudml.org/doc/271225
ER -

References

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  1. [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[Crossref] Zbl1051.05053
  2. [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. [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[Crossref] 
  4. [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[Crossref][WoS] Zbl1293.05183
  5. [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 [Crossref] Zbl1306.05121

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