Independent Transversals versus Transversals

Konrad K. Dabrowski, Matthew Johnson, Giacomo Paesani, Daniel Paulusma, Viktor Zamaraev

Abstract: We compare the minimum size of a vertex cover, feedback vertex set and odd cycle transversal of a graph with the minimum size of the corresponding variants in which the transversal must be an independent set. We investigate for which graphs $H$ the two sizes are equal whenever the graph in question belongs to the class of $H$-free graphs. We find complete classifications for vertex cover and almost complete classifications for feedback vertex set and odd cycle transversal.