Wszystkie pola: degree theory - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Large Degree Vertices in Longest Cycles of Graphs, I
Autorzy:: Li, Binlong
Xiong, Liming
Yin, Jun
Powiązania:: https://bibliotekanauki.pl/articles/31340944.pdf
Data publikacji:: 2016-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: longest cycle
large degree vertices
order
connectivity
independent number
Opis:: In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 2; 363-382
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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

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