An implementable Three-in-a-tree algorithm to accelerate Perfect Graph detection

In this thesis we implement the algorithm of Chudnovsky et al.(2005) to determine if a given graph contains an odd-hole or anti-hole. In particular this decides whether a given graph is perfect according to the strong perfect graph theorem proved by Chudnovsky et al. (2006). A main bottleneck of this algorithm is the detection of pyramids in a given graph. We introduce the three-in-a-tree problem and develop new sub-algorithms to make the decision algorithm of Lai et al. (2020) self-standing and not based on other highly theoretical results. This new algorithm allows us to actually implement the three-in-a-tree algorithm and also leads to a reduced running time of detecting pyramids by three orders of magnitude.