On diameters and radii of bridged graphs
Discrete Mathematics
Computing independent sets in graphs with large girth
Discrete Applied Mathematics
Large 2P3-free graphs with bounded degree
Discrete Mathematics - Special issue: selected papers in honour of Paul Erdo&huml;s on the occasion of his 80th birthday
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
New results on induced matchings
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Independent Sets in Asteroidal Triple-Free Graphs
SIAM Journal on Discrete Mathematics
Determining DNA Sequence Similarity Using Maximum Independent Set Algorithms for Interval Graphs
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Induced Matchings in Regular Graphs and Trees
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Finding a maximum induced matching in weakly chordal graphs
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Induced matchings in asteroidal triple-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Polynomial algorithm for finding the largest independent sets in graphs without forks
Discrete Applied Mathematics
Satgraphs and independent domination: part 1
Theoretical Computer Science
A polynomial algorithm to find an independent set of maximum weight in a fork-free graph
Journal of Discrete Algorithms
Note: On the inapproximability of independent domination in 2P3-free perfect graphs
Theoretical Computer Science
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
Parameterized complexity of finding regular induced subgraphs
Journal of Discrete Algorithms
Independent sets in extensions of 2K2-free graphs
Discrete Applied Mathematics
Independent Sets of Maximum Weight in Apple-Free Graphs
SIAM Journal on Discrete Mathematics
On distance-3 matchings and induced matchings
Discrete Applied Mathematics
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
Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time
Theoretical Computer Science
Hi-index | 5.23 |
Finding maximum regular induced subgraphs is a family of algorithmic graph problems containing several important representatives such as maximum independent set, maximum clique, and maximum induced matching. These problems are generally NP-hard. On the other hand, each of them may become polynomially solvable when restricted to graphs in special classes. However, polynomial-time solutions are available only for very few monogenic classes, i.e. classes defined by a single forbidden induced subgraph. Only three such results are available for the maximum independent set and maximum clique problems and only two for the maximum induced matching problem. In the present paper, we extend this restricted list of results by exploring the complexity of the problems in the class of 2P"3-free graphs, which recently attracted considerable attention in the literature. By elaborating a polynomial-time solution to the maximum independent set problem in the class of 2K"2-free graphs proposed by Farber in [16], we show that both maximum independent set (0-regular induced subgraph) and maximum induced matching(1-regular induced subgraph) are solvable in polynomial time for 2P"3-free graphs. We also conjecture that the same is true for finding maximum k-regular induced subgraphs for each value of k. On the other hand, we conjecture that finding a maximum subset of vertices inducing the complement of a k-regular induced subgraph is NP-hard for 2P"3-free graphs and verify the conjecture for k=0 (maximum clique), k=1 (maximum induced co-matching), and k=2.