User:Abdul Muhsy/sandbox

In graph theory the Welsh-Powell algorithm, also known as the Welch-Powell algorithm is an algorithm given by Welsh and Powell which yields an upper bound for the chromatic number of a graph. More specifically, given a finite graph on $$n$$ vertices and degree sequence $$d_1\ge d_2\ge\cdots\ge d_n$$, the Welsh-Powell algorithm applies the greedy algorithm to the vertices in nondecreasing order of degree. This ultimately yields the bound $$\chi(G)\le \max_i\min\{d_i,i+1\}$$. The Welsh-Powell algorithm was initially devised to solve the problem of determining a particular scheduling problem - specifically that of determining the minimum number of days required to perform $$n$$ jobs when some of the jobs cannot be performed simultaneously. The connection between the chromatic number and scheduling, which was discussed in the same article in which the Welsh-Powell algorithm was introduced, has been prominent in scheduling and timetabling research ever since.