Long cycles in graphs with no subgraphs of minimal degree 3
Discrete Mathematics
Induced subgraphs of the power of a cycle
SIAM Journal on Discrete Mathematics
The complexity of regular subgraph recognition
Discrete Applied Mathematics - Computational combinatiorics
Discrete Mathematics
Finding regular subgraphs in both arbitrary and planar graphs
Discrete Applied Mathematics
Deciding first-order properties of locally tree-decomposable structures
Journal of the ACM (JACM)
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
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
Networks
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
The parameterized complexity of regular subgraph problems and generalizations
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
The complexity of uniform Nash equilibria and related regular subgraph problems
Theoretical Computer Science
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Degree-Constrained Subgraph Problems: Hardness and Approximation Results
Approximation and Online Algorithms
Finding Dense Subgraphs with Size Bounds
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Parameterized complexity of finding regular induced subgraphs
Journal of Discrete Algorithms
Hardness and approximation of traffic grooming
Theoretical Computer Science
Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs
Journal of Discrete Algorithms
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
On the approximability of some degree-constrained subgraph problems
Discrete Applied Mathematics
Increasing the minimum degree of a graph by contractions
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On approximating the d-girth of a graph
Discrete Applied Mathematics
Hi-index | 0.00 |
In this article we study the parameterized complexity of problems consisting in finding degree-constrained subgraphs, taking as the parameter the number of vertices of the desired subgraph. Namely, given two positive integers d and k, we study the problem of finding a d-regular (induced or not) subgraph with at most k vertices and the problem of finding a subgraph with at most k vertices and of minimum degree at least d. The latter problem is a natural parameterization of the d-girth of a graph (the minimum order of an induced subgraph of minimum degree at least d). We first show that both problems are fixed-parameter intractable in general graphs. More precisely, we prove that the first problem is W[1]-hard using a reduction from Multi-Color Clique. The hardness of the second problem (for the non-induced case) follows from an easy extension of an already known result. We then provide explicit fixed-parameter tractable (FPT) algorithms to solve these problems in graphs with bounded local treewidth and graphs with excluded minors, using a dynamic programming approach. Although these problems can be easily defined in first-order logic, hence by the results of Frick and Grohe (2001) [23] are FPT in graphs with bounded local treewidth and graphs with excluded minors, the dependence on k of our algorithms is considerably better than the one following from Frick and Grohe (2001) [23].