MapReduce is a common programming model for processing and generating large datasets at present. Using the model, the programming for distributed computing can be easier than others. The extremal graph is a graph with the maximum number of edges such that it does not contain given sub graph. The method of constructing extremal graphs is an important research content in Graph Theory. The algorithm of constructing extremal graphs based on the MapReduce programming model is studied in this paper. By mapping the key-value pairs of MapReduce model properly, the parallel constructing algorithms are designed and implemented. Finally, we construct extremal graphs not containing hexagons and with no more than 26 vertices using the algorithm. By the results of experiments, it is showed that the average speedup is 2.55, and the average efficiency is 85%.
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