Název:	Long paths and toughness of k-trees and chordal planar graphs
Autoři:	Kabela, Adam
Citace zdrojového dokumentu:	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.
Datum vydání:	2019
Nakladatel:	Elsevier
Typ dokumentu:	postprint postprint
URI:	2-s2.0-85054444831 http://hdl.handle.net/11025/30772
ISSN:	0012-365X
Klíčová slova v dalším jazyce:	k-trees;Chordal planar graphs;Hamilton-connectedness;Shortness exponent;Toughness
Abstrakt v dalším jazyce:	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.
Práva:	© Elsevier
Vyskytuje se v kolekcích:	Postprinty / Postprints (KMA) OBD

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