Abstract
We prove that finding a k-edge induced subgraph is fixed-parameter tractable, thereby answering an open problem of Leizhen Cai [2]. Our algorithm is based on several combinatorial observations, Gauss’ famous Eureka theorem [1], and a generalization of the wellknown fpt-algorithm for the model-checking problem for first-order logic on graphs with locally bounded tree-width due to Frick and Grohe [13]. On the other hand, we show that two natural counting versions of the problem are hard. Hence, the k-edge induced subgraph problem is one of the very few known examples in parameterized complexity that are easy for decision while hard for counting.
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Lin, B., Chen, Y. (2012). The Parameterized Complexity of k-Edge Induced Subgraphs. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_54
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