A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs

• Autorzy: Wojciech Wide
• Języki publikacji: EN

Abstrakty

EN

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), dK(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 {K1,3, P7, D}-f1-heavy graph on n ≥ 14 vertices is pancyclic. This result extends the previous work by Faudree, Ryjáček and Schiermeyer.

Słowa kluczowe

EN

cycle; Fan-type heavy subgraph; Hamilton cycle; pancyclicity

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 2
• Strony: 477-499

Daty

wydano

2017-05-01

otrzymano

2015-10-20

poprawiono

2016-02-01

zaakceptowano

2016-02-01

online

2017-04-01

Twórcy

autor

Wojciech Wide

• Faculty of Applied Mathematics Department of Discrete Mathematics AGH University of Science and Technology al. Mickiewicza 30, 30–059 Krakow,

Identyfikatory

DOI

10.7151/dmgt.1938