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A note on longest paths in circular arc graphs. (English) Zbl 1317.05102

Summary: As observed by D. Rautenbach and J.-S. Sereni [SIAM J. Discrete Math. 28, No. 1, 335–341 (2014; Zbl 1293.05183)] there is a gap in the proof of the theorem of P. N. Balister et al. [Comb. Probab. Comput. 13, No. 3, 311–317 (2004; Zbl 1051.05053)], which states that the intersection of all longest paths in a connected circular arc graph is nonempty. In this paper, we close this gap.

MSC:

05C38 Paths and cycles
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References:

[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 · Zbl 1051.05053
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[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 · Zbl 1293.05183
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