Title: | Bounding the distance among longest paths in a connected graph |
Authors: | Ekstein, Jan Fujita, Shinya Kabela, Adam Teska, Jakub |
Citation: | EKSTEIN, J., FUJITA, S., KABELA, A., TESKA, J. Bounding the distance among longest paths in a connected graph. DISCRETE MATHEMATICS, 2018, roč. 341, č. 4, s. 1155-1159. ISSN: 0012-365X |
Issue Date: | 2018 |
Publisher: | Elsevier |
Document type: | postprint postprint |
URI: | 2-s2.0-85033482578 http://hdl.handle.net/11025/29791 |
ISSN: | 0012-365X |
Keywords in different language: | Longest paths;Path intersection |
Abstract in different language: | It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k >= 7, Skupień in 1966 obtained a connected graph in which some longest paths have no common vertex, but every k - 1 longest paths have a common vertex. It is not known whether every 3 longest paths in a connected graph have a common vertex and similarly for 4, 5, and 6 longest path. Fujita et al. in 2015 give an upper bound on distance among 3 longest paths in a connected graph. In this paper we give a similar upper bound on distance between 4 longest paths and also for k longest paths, in general. |
Rights: | © Elsevier |
Appears in Collections: | Články / Articles (KMA) OBD |
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1607.08850v2.pdf | 148,75 kB | Adobe PDF | View/Open |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11025/29791
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