Journal of Combinatorial Theory Series B
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Hardness and approximation of traffic grooming
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Traffic grooming in WDM networks: past and future
IEEE Network: The Magazine of Global Internetworking
Connected coloring completion for general graphs: algorithms and complexity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Multiple Hypernode Hitting Sets and Smallest Two-Cores with Targets
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Degree-Constrained Subgraph Problems: Hardness and Approximation Results
Approximation and Online Algorithms
On approximating the d-girth of a graph
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Tight complexity bounds for FPT subgraph problems parameterized by clique-width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Finding dense subgraphs of sparse graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems
Theoretical Computer Science
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In this paper we study the problem of finding an induced subgraphof size at most k with minimum degree at least d for a given graphG, from the parameterized complexity perspective. We call this problemMinimum Subgraph of Minimum Degree ≥d (MSMDd). For d = 2 itcorresponds to finding a shortest cycle of the graph. Our main motivationto study this problem is its strong relation to Dense k-Subgraphand Traffic Grooming problems. First, we show that MSMSd is fixed-parameter intractable (providedFPT ≠ W[1]) for d ≥ 3 in general graphs, by showing it to be W[1]-hardusing a reduction from Multi-Color Clique. In the second part of thepaper we provide explicit fixed-parameter tractable (FPT) algorithmsfor the problem in graphs with bounded local tree-width and graphswith excluded minors, faster than those coming from the meta-theorem of Frick and Grohe [13] about problems definable in first order logicover "locally tree-decomposable structures". In particular, this impliesfaster fixed-parameter tractable algorithms in planar graphs, graphs ofbounded genus, and graphs with bounded maximum degree.