The document describes two graph coloring algorithms: the greedy coloring algorithm which colors each vertex with the first available color while ensuring no adjacent vertices share a color, and the Welsh Powell algorithm which orders vertices by descending degree, colors the highest degree vertex first, then colors remaining vertices the same color if not adjacent to previously colored vertices before moving on to the next color. An example of the Welsh Powell algorithm applied to the vertices K,G,I,J,A,B,F,C is also provided.

1. Graph coloring algorithm
Sanjana Urmy
13CSE030

2. Greedy coloring algorithm
1. Choose an order for the vertices.
2. Choose a list of colors , also in same order.
3.In order , color each vertex using the first
available color on the list , making sure that no
two adjacent vertices are the same color.
4.Continue in this way until each vertex is
colored.

11. Welsh Powell Algorithm
• Find the degree of each vertex
• List the verices in order of descending
valence. Colour the first vertex in the list
• Go down the sorted list and color every vertex
not connected to the colored vertices above
the same color then cross out all colored
vertices in the list.
• Repeat the process on the uncolored vertices
with a new color-always working in
descending order of degree until all vertices
are colored.

12. Welsh Powell Algorithm: Example

16. K,G,I,J,A,B,F,C.

22. G,J,B