- Tytuł:
- 2-Connected Hamiltonian Claw-Free Graphs Involving Degree Sum of Adjacent Vertices
- Autorzy:
-
Tian, Tao
Xiong, Liming - Powiązania:
- https://bibliotekanauki.pl/articles/32034090.pdf
- Data publikacji:
- 2020-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Hamiltonian cycle
degree sum
dominating closed trail
closure - Opis:
- For a graph H, define $\overline{\sigma}_2(H)=min\{d(u)+d(v)|uv∈E(H)\}$. Let $H$ be a 2-connected claw-free simple graph of order $n$ with \(\delta(H) ≥ 3\). In [J. Graph Theory 86 (2017) 193–212], Chen proved that if $\overline{\sigma}_2(H)≥\frac{n}{2}−1$ and $n$ is sufficiently large, then $H$ is Hamiltonian with two families of exceptions. In this paper, we refine the result. We focus on the condition $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$, and characterize non-Hamiltonian 2-connected claw-free graphs $H$ of order $n$ sufficiently large with $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$. As byproducts, we prove that there are exactly six graphs in the family of 2-edge-connected triangle-free graphs of order at most seven that have no spanning closed trail and give an improvement of a result of Veldman in [Discrete Math. 124 (1994) 229–239].
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 85-106
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł