Temat: Hamilton cycle - 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

Skocz do pozycji: 3.

Tytuł:: Edge condition for hamiltonicity in balanced tripartite graphs
Autorzy:: Adamus, J.
Powiązania:: https://bibliotekanauki.pl/articles/255875.pdf
Data publikacji:: 2009
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Hamilton cycle
pancyclicity
tripartite graph
edge condition
Opis:: A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order 2n obtained from the complete balanced bipartite Kn,n by removing at most n - 2 edges, is bipancyclic. We prove an analogous result for balanced tripartite graphs: If G is a balanced tripartite graph of order 3n and size at least 3n(2) - 2n + 2, then G contains cycles of all lengths.
Źródło:: Opuscula Mathematica; 2009, 29, 4; 337-343
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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