Long paths and toughness of k-trees and chordal planar graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43953232" target="_blank" >RIV/49777513:23520/19:43953232 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0012365X18302759?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0012365X18302759?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2018.08.017" target="_blank" >10.1016/j.disc.2018.08.017</a>

Result language
angličtina
Original language name
Long paths and toughness of k-trees and chordal planar graphs
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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