Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
The Parameterized Complexity of Counting Problems
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On Parameterized Path and Chordless Path Problems
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Understanding the Complexity of Induced Subgraph Isomorphisms
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Deciding First-Order Properties for Sparse Graphs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Random separation: a new method for solving fixed-cardinality optimization problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized Complexity
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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.