A Note on Longest Paths in Circular Arc Graphs
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 pa...
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Sciendo
2015-08-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1800 |
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doaj-35882f9e67384b13a8c906d8f145d93c2021-09-05T17:20:21ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922015-08-0135341942610.7151/dmgt.1800dmgt.1800A Note on Longest Paths in Circular Arc GraphsJoos Felix0Institut für Optimierung und Operations Research Universität Ulm, Ulm, GermanyAs 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.https://doi.org/10.7151/dmgt.1800circular arc graphslongest paths intersection |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Joos Felix |
| spellingShingle |
Joos Felix A Note on Longest Paths in Circular Arc Graphs Discussiones Mathematicae Graph Theory circular arc graphs longest paths intersection |
| author_facet |
Joos Felix |
| author_sort |
Joos Felix |
| title |
A Note on Longest Paths in Circular Arc Graphs |
| title_short |
A Note on Longest Paths in Circular Arc Graphs |
| title_full |
A Note on Longest Paths in Circular Arc Graphs |
| title_fullStr |
A Note on Longest Paths in Circular Arc Graphs |
| title_full_unstemmed |
A Note on Longest Paths in Circular Arc Graphs |
| title_sort |
note on longest paths in circular arc graphs |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2015-08-01 |
| description |
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. |
| topic |
circular arc graphs longest paths intersection |
| url |
https://doi.org/10.7151/dmgt.1800 |
| work_keys_str_mv |
AT joosfelix anoteonlongestpathsincirculararcgraphs AT joosfelix noteonlongestpathsincirculararcgraphs |
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1717786495054512128 |