Certifying Induced Subgraphs in Large Graphs

We introduce I/O-effiient certifying algorithms for bipartite graphs, as well the classes of split, threshold, chain, and trivially perfect graphs. When input graph is a member respective class, algorithm returns certificate that characterizes this class. Otherwise, it forbidden induced subgraph non-membership. On with n vertices m edges, our take $$O( {\textsc {sort}(n + m)} ) $$ I/Os in worst case threshold In same complexity chain graphs can be certified high probability. provide implementations split preliminary experimental evaluation.