Temat: Fan-type heavy subgraph - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs
Autorzy:: Wideł, Wojciech
Powiązania:: https://bibliotekanauki.pl/articles/31341120.pdf
Data publikacji:: 2016-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: cycle
Fan-type heavy subgraph
Hamilton cycle
pancyclicity
Opis:: Let $G$ be a graph on $n$ vertices and let $H$ be a given graph. We say that $G$ is pancyclic, if it contains cycles of all lengths from 3 up to $n$, and that it is $H-f_1$-heavy, if for every induced subgraph $K$ of $G$ isomorphic to $H$ and every two vertices $u, v \in V (K)$, $d_K(u, v) = 2$ implies $ \text{min} \{ d_G(u), d_G(v) \} \ge \frac{n+1}{2} $. In this paper we prove that every 2-connected $ \{ K_{1,3} , P_5}-f_1$-heavy graph is pancyclic. This result completes the answer to the problem of finding $ f_1 $-heavy pairs of subgraphs implying pancyclicity of 2-connected graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 1; 173-184
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
Autorzy:: Wide, Wojciech
Powiązania:: https://bibliotekanauki.pl/articles/31341826.pdf
Data publikacji:: 2017-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: cycle
Fan-type heavy subgraph
Hamilton cycle
pancyclicity
Opis:: A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . ., n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f₁-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), d_K(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs ℋ we say that G is ℋ-f₁-heavy, if G is H-f₁-heavy for every graph H ∈ℋ. Let D denote the deer, a graph consisting of a triangle with two disjoint paths P3 adjoined to two of its vertices. In this paper we prove that every 2-connected {K_1,3, P₇, D}-f₁-heavy graph on n ≥ 14 vertices is pancyclic. This result extends the previous work by Faudree, Ryjáček and Schiermeyer.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 2; 477-499
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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