- Tytuł:
- A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
- Autorzy:
-
Tang, Long
Vumar, Elkin - Powiązania:
- https://bibliotekanauki.pl/articles/32032199.pdf
- Data publikacji:
- 2020-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
locally connected
locally Hamiltonian
locally Hamilton-connected
fully cycle extendability
weakly pancyclicity - Opis:
- Let \(\mathcal{P}\) be a property of a graph. A graph G is said to be locally \(\mathcal{P}\), if the subgraph induced by the open neighbourhood of every vertex in G has property \(\mathcal{P}\). Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic. Motivated by the above conjecture, van Aardt et al. [S.A.van Aardt, M. Frick, O.R. Oellermann and J.P.de Wet, Global cycle properties in locally connected, locally traceable and locally Hamiltonian graphs, Discrete Appl. Math. 205 (2016) 171–179] investigated the global cycle structures in connected, locally traceable/Hamiltonian graphs. Among other results, they proved that a connected, locally Hamiltonian graph G with maximum degree at least |V (G)| − 5 is weakly pancyclic. In this note, we improve this result by showing that such a graph with maximum degree at least |V (G)|−6 is weakly pancyclic. Furthermore, we show that a connected, locally Hamilton-connected graph with maximum degree at most 7 is fully cycle extendable.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 77-84
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł