Is it FPT to cover points with tours on minimum number of bends (Errata)?

Abstract

Recent communication by Minghui Jiang has brought to my attention that I overlooked faults in the arguments built while collaborating closely with my PhD student Apichat Heednacram and his co-supervisor Francis Suraweera. These errors unfortunately also escaped the scrutiny of peer-reviews and the formal process of examination. Some results in Apichat's dissertation that were published in this journal (and other outlets) are actually incorrect. In particular, we had reported an FPT-algorithms for the k-Bends Traveling Salesman Problem in 2 and some variants that result from adding constraints to the line-segments that constitute the tour. While the reduction rules to kernelize the problem produce reduced instances, a solution of the kernel instance does not lead directly to a solution of the original instance.