I am a research scholar, currently working on parameterized algorithms. I am working on a problem and have been exploring various parameters for which the problem remains unsolved. I have read the following paper on formulating fixed parameter tractable algorithms for Twin cover.
1.Ganian, Robert, Twin-cover: beyond vertex cover in parameterized algorithmics, Marx, Dániel (ed.) et al., Parameterized and exact computation. 6th international symposium, IPEC 2011, Saarbrücken, Germany, September 6–8, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-28049-8/pbk). Lecture Notes in Computer Science 7112, 259-271 (2012). ZBL1352.68105.
Even though i understand all the techniques described in this paper, I did not understand how a problem is fixed parameter tractable with respect to a larger parameter(vertex cover in this case) if it is fixed parameter tractable with respect to a smaller parameter(twin cover in this case). The problem i am working on is proved to be fixed parameter tractable with respect to the vertex cover and it is open when parameterized by twin cover. Could someone elaborate on this?