Induced Subgraph Saturated Graphs
A graph $G$ is said to be \emph{$H$-saturated} if $G$ contains no subgraph isomorphic to $H$ but the addition of any edge between non-adjacent vertices in $G$ creates one. While induced subgraphs are often studied in the extremal case with regard to the removal of edges, we extend saturation to indu...
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| Format: | Article |
| Language: | English |
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Georgia Southern University
2016-01-01
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| Series: | Theory and Applications of Graphs |
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| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol3/iss2/1 |
| Summary: | A graph $G$ is said to be \emph{$H$-saturated} if $G$ contains no subgraph isomorphic to $H$ but the addition of any edge between non-adjacent vertices in $G$ creates one. While induced subgraphs are often studied in the extremal case with regard to the removal of edges, we extend saturation to induced subgraphs. We say that $G$ is \emph{induced $H$-saturated} if $G$ contains no induced subgraph isomorphic to $H$ and the addition of any edge to $G$ results in an induced copy of $H$. We demonstrate constructively that there are non-trivial examples of saturated graphs for all cycles and an infinite family of paths and find a lower bound on the size of some induced path-saturated graphs. |
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| ISSN: | 2470-9859 |