Parameterized Complexity of Eulerian Deletion Problems

Marek Cygan, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, Ildikó Schlotter

Abstract: We study a family of problems where the goal is to make a graph Eulerian by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions, with or without the requirement of connectivity, etc. Of particular interest is a randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges.