Long paths and toughness of k-trees and chordal planar graphs
| dc.contributor.author | Kabela, Adam | |
| dc.date.accessioned | 2019-01-14T11:00:09Z | |
| dc.date.available | 2019-01-14T11:00:09Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract-translated | We show that every k-tree of toughness greater than k/3 is Hamilton-connected for k >= 3. (In particular, chordal planar graphs of toughness greater than 1 are Hamilton-connected.) This improves the result of Broersma et al. (2007) and generalizes the result of Böhme et al. (1999). On the other hand, we present graphs whose longest paths are short. Namely, we construct 1-tough chordal planar graphs and 1-tough planar 3-trees, and we show that the shortness exponent of the class is 0, at most log_{30}22, respectively. Both improve the bound of Böhme et al. Furthermore, the construction provides k-trees (for k >= 4) of toughness greater than 1. | en |
| dc.format | 9 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | KABELA, A. Long paths and toughness of k-trees and chordal planar graphs. DISCRETE MATHEMATICS, 2019, roč. 342, č. 1, s. 55-63. ISSN 0012-365X. | en |
| dc.identifier.document-number | 451939300006 | |
| dc.identifier.doi | 10.1016/j.disc.2018.08.017 | |
| dc.identifier.issn | 0012-365X | |
| dc.identifier.obd | 43924231 | |
| dc.identifier.uri | 2-s2.0-85054444831 | |
| dc.identifier.uri | http://hdl.handle.net/11025/30772 | |
| dc.language.iso | en | en |
| dc.project.ID | LO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost | cs |
| dc.project.ID | GA17-04611S/Ramseyovské aspekty barvení grafů | cs |
| dc.project.ID | SGS-2016-003/Kvalitativní a kvantitativní studium matematických modelů III. | cs |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | Discrete Mathematics | en |
| dc.rights | © Elsevier | en |
| dc.rights.access | openAccess | en |
| dc.subject.translated | k-trees | en |
| dc.subject.translated | Chordal planar graphs | en |
| dc.subject.translated | Hamilton-connectedness | en |
| dc.subject.translated | Shortness exponent | en |
| dc.subject.translated | Toughness | en |
| dc.title | Long paths and toughness of k-trees and chordal planar graphs | en |
| dc.type | postprint | cs |
| dc.type | postprint | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | acceptedVersion | en |