Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Deciding whether a planar graph has a cubic subgraph is NP-complete
Discrete Mathematics
Finding regular subgraphs in both arbitrary and planar graphs
Discrete Applied Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On locating cubic subgraphs in bounded-degree connected bipartite graphs
Discrete Mathematics
Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Strong Lower Bounds on the Approximability of some NPO PB-Complete Maximization Problems
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
The Approximation of Maximum Subgraph Problems
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
Approximability results for the maximum and minimum maximal induced matching problems
Discrete Optimization
Algorithmic Meta-theorems for Restrictions of Treewidth
Algorithmica - Special Issue: Parameterized and Exact Computation, Part I
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We study the problem of finding a maximum vertex-subset S of a given graph G such that the subgraph G[S] induced by S is r-regular for a prescribed degree r≥0. We also consider a variant of the problem which requires G[S] to be r-regular and connected. Both problems are known to be NP-hard even to approximate for a fixed constant r. In this paper, we thus consider the problems whose input graphs are restricted to some special classes of graphs. We first show that the problems are still NP-hard to approximate even if r is a fixed constant and the input graph is either bipartite or planar. On the other hand, both problems are tractable for graphs having tree-like structures, as follows. We give linear-time algorithms to solve the problems for graphs with bounded treewidth; we note that the hidden constant factor of our running time is just a single exponential of the treewidth. Furthermore, both problems are solvable in polynomial time for chordal graphs.