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Let H be a family of simple graphs and k be a positive integer. We say that a graph G of order n ≥ k satisfies Fan's condition with respect to H with constant k, if for every induced subgraph H of G isomorphic to any of the graphs from H the following holds:doi:10.7494/opmath.2017.37.4.617 fatcat:n6vlbpgpmzb37puyipemnhko6a