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Problem of finding an optimal upper bound for the chromatic no. of even3K1-free graphs is still open and pretty hard. Here we prove Borodin &Kostochka Conjecture for 4K1-free graphs G i.e. If maximum degree of a {4 TimesK1}-free graph is greater than or equal to 9, then the chromatic number of thegraph is less than or equal to maximum of {\omega} and {\delta-1}.

Validity of Borodin and Kostochka Conjecture for {4 Times K1}-free Graphs