On a local similarity of graphs

Edit distance measure for graphs

“…They invastigate the following problem: given integers n, e, e ′ , what is the largest number g(n, e, e ′ ) such that any two n vertex graphs G and H, with e and e ′ edges respectively, must have a common subgraph with at least g(n, e, e ′ ) edges. Another Ramsey like similarity measure was introduced by Dzido and Krzywdzinski in [9]. The authors consider the problem of finding the smallest n to ensure at least one k-similar pair in any family of l graphs on n vertices.…”

“…The authors consider the problem of finding the smallest n to ensure at least one k-similar pair in any family of l graphs on n vertices. In [9] two graphs G and H, having the same number of vertices n, are k-similar if they contain a common induced subgraph of order k.…”