A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
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 isomo...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2017-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1938 |
| _version_ | 1797704423866105856 |
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| author | Wide Wojciech |
| author_facet | Wide Wojciech |
| author_sort | Wide Wojciech |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T05:20:12Z |
| format | Article |
| id | doaj.art-d491d6556abb46f8be002a38f6bfca74 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T05:20:12Z |
| publishDate | 2017-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-d491d6556abb46f8be002a38f6bfca742023-09-03T07:47:21ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922017-05-0137247749910.7151/dmgt.1938dmgt.1938A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected GraphsWide Wojciech0Faculty of Applied Mathematics Department of Discrete Mathematics AGH University of Science and Technology al. Mickiewicza 30, 30–059 Krakow, PolandA 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.https://doi.org/10.7151/dmgt.1938cyclefan-type heavy subgraphhamilton cyclepancyclicity |
| spellingShingle | Wide Wojciech A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs Discussiones Mathematicae Graph Theory cycle fan-type heavy subgraph hamilton cycle pancyclicity |
| title | A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs |
| title_full | A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs |
| title_fullStr | A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs |
| title_full_unstemmed | A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs |
| title_short | A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs |
| title_sort | triple of heavy subgraphs ensuring pancyclicity of 2 connected graphs |
| topic | cycle fan-type heavy subgraph hamilton cycle pancyclicity |
| url | https://doi.org/10.7151/dmgt.1938 |
| work_keys_str_mv | AT widewojciech atripleofheavysubgraphsensuringpancyclicityof2connectedgraphs AT widewojciech tripleofheavysubgraphsensuringpancyclicityof2connectedgraphs |