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- W2737977639 abstract "We show that every $k$-tree of toughness greater than $frac{k}{3}$ is Hamilton-connected for $k geq 3$. (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 Bohme 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 Bohme et al. Furthermore, the construction provides $k$-trees (for $k geq 4$) of toughness greater than $1$." @default.
- W2737977639 created "2017-07-31" @default.
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- W2737977639 date "2017-07-25" @default.
- W2737977639 modified "2023-09-27" @default.
- W2737977639 title "Long paths and toughness of k-trees and chordal planar graphs" @default.
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