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A graph is an interval graph iff it is chordal and asteroidal triple free. An interval graph is proper interval graph iff it is $K_{1,3}$ free.

However i googled intensely to find a minimal set of forbidden subgraphs for proper interval graphs,but in vain.

My question is : What are the minimal set of forbidden subgraphs for proper interval graphs ? Any link to journal/paper is welcome.

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up vote 6 down vote accepted

ISGCI's page on proper interval graphs (from our FAQ) lists a few equivalent classes; one of them is the class of $(C_{n+4}$, $S_3$, claw, net)-free graphs (see the same website for definitions).

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