The extremal function for complete minors
Journal of Combinatorial Theory Series B
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
On Independent Sets and Bicliques in Graphs
Graph-Theoretic Concepts in Computer Science
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
The Complexity of Satisfiability of Small Depth Circuits
Parameterized and Exact Computation
Exact and approximate bandwidth
Theoretical Computer Science
On the possibility of faster SAT algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Breaking the 2n-barrier for Irredundance: Two lines of attack
Journal of Discrete Algorithms
Enumerating minimal subset feedback vertex sets
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Exact algorithm for the maximum induced planar subgraph problem
ESA'11 Proceedings of the 19th European conference on Algorithms
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Fast exponential algorithms for maximum γ-regular induced subgraph problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Exact computation of maximum induced forest
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Partitioning based algorithms for some colouring problems
CSCLP'05 Proceedings of the 2005 Joint ERCIM/CoLogNET international conference on Constraint Solving and Constraint Logic Programming
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
| Hi-index | 0.00 |
In this paper we study the problem of finding a maximum induced d-degenerate subgraph in a given n-vertex graph from the point of view of exact algorithms. We show that for any fixed d one can find a maximum induced d-degenerate subgraph in randomized $(2-\varepsilon _d)^nn^{\mathcal{O}(1)}$ time, for some constant εd0 depending only on d. Moreover, our algorithm can be used to sample inclusion-wise maximal induced d-degenerate subgraphs in such a manner that every such subgraph is output with probability at least (2−εd)−n; hence, we prove that their number is bounded by (2−εd)n.