  Problem of finding an optimal upper bound for the chromatic no. of a graph is
still open and very hard. Borodin and Kostochka Conjecture is still open and if
proved will improve Brook bound on Chromatic no. of a graph. Here we prove
Borodin & Kostochka Conjecture for (1) (P4 Union K1)-free (2) P5-free (3)
Chair-free graphs and 4) graphs with dense neighbourhoods. Certain known
results follow as Corollaries.
