3 research outputs found
Induced Subgraph Saturated Graphs
A graph is said to be \emph{-saturated} if contains no subgraph isomorphic to but the addition of any edge between non-adjacent vertices in 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 is \emph{induced -saturated} if contains no induced subgraph isomorphic to and the addition of any edge to results in an induced copy of . 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