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Chordal Graphs

(suggested content)

(due 10pm Nov 24)

1. Definitions

• Chordal graphs
• Simplicial vertices
• Simplicial elimination orderings (a.k.a., perfect elimination orderings)
• Minimal separators (a.k.a., minimal vertex cuts)
• Examples to illustrates the concepts

2. Characterizations of chordal graphs in terms of

• the existence of simplicial vertices
• the existence of simplicial orderings
• minimal separators
• subtrees in a tree

3. Maximum independent set problem and minimum colouring problem

• Algorithm for finding a maximum independent set in a chordal graph
• Algorithm for colouring a chordal graph optimally

4. References