The Parameterized Complexity of k-Edge Induced Subgraphs

  • Bingkai Lin
  • Yijia Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


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.


Parameterized Complexity Computable Function Relation Symbol Counting Problem Induce Subgraph 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bingkai Lin
    • 1
  • Yijia Chen
    • 1
  1. 1.Shanghai Jiao Tong Universitychina

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