Parameterized Complexity of Even/Odd Subgraph Problems
In this paper, we investigate the parameterized complexity of the problem of finding k edges (vertices) in a graph G to form a subgraph (respectively, induced subgraph) H such that H belongs to one the following four classes of graphs: even graphs, Eulerian graphs, odd graphs, and connected odd graphs. We also study the parameterized complexity of their parametric dual problems. Among these sixteen problems, we show that eight of them are fixed parameter tractable and four are W-hard. Our main techniques are the color-coding method of Alon, Yuster and Zwick, and the random separation method of Cai, Chan and Chan.
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