Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
Let G be a graph on n vertices. A vertex of G with degree at least n/2 is called a heavy vertex, and a cycle of G which contains all the heavy vertices of G is called a heavy cycle. In this note, we characterize graphs which contain no heavy cycles. For a given graph H, we say that G is H-heavy if e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2016-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1863 |
| Summary: | Let G be a graph on n vertices. A vertex of G with degree at least n/2 is called a heavy vertex, and a cycle of G which contains all the heavy vertices of G is called a heavy cycle. In this note, we characterize graphs which contain no heavy cycles. For a given graph H, we say that G is H-heavy if every induced subgraph of G isomorphic to H contains two nonadjacent vertices with degree sum at least n. We find all the connected graphs S such that a 2-connected graph G being S-heavy implies any longest cycle of G is a heavy cycle. |
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| ISSN: | 2083-5892 |