Journal of Algorithms
On claw-free asteroidal triple-free graphs
Discrete Applied Mathematics
LexBFS-Ordering in Asteroidal Triple-Free Graphs
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
On linear and circular structure of (claw, net)-free graphs
Discrete Applied Mathematics
Induced matchings in asteroidal triple-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Algorithms for graphs with small octopus
Discrete Applied Mathematics
Improved bottleneck domination algorithms
Discrete Applied Mathematics
Information Sciences: an International Journal
Maximum independent sets in graphs of low degree
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Feedback vertex set on AT-free graphs
Discrete Applied Mathematics
Note: On the inapproximability of independent domination in 2P3-free perfect graphs
Theoretical Computer Science
On Distance-3 Matchings and Induced Matchings
Graph Theory, Computational Intelligence and Thought
On distance-3 matchings and induced matchings
Discrete Applied Mathematics
Separator orders in interval, cocomparability, and AT-free graphs
Discrete Applied Mathematics
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Reduced clique graphs of chordal graphs
European Journal of Combinatorics
Approximability results for the maximum and minimum maximal induced matching problems
Discrete Optimization
The black-and-white coloring problem on distance-hereditary graphs and strongly chordal graphs
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Induced disjoint paths in AT-Free graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Maximum regular induced subgraphs in 2P3-free graphs
Theoretical Computer Science
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On the stable degree of graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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An asteroidal triple (AT) is a set of three vertices such that there is a path between any pair of them avoiding the closed neighborhood of the third. A graph is called AT-free if it does not have an AT. We show that there is an O(n4) time algorithm to compute the maximum weight of an independent set for AT-free graphs. Furthermore, we obtain O(n4) time algorithms to solve the INDEPENDENT DOMINATING SET and the INDEPENDENT PERFECT DOMINATING SET problems on AT-free graphs. We also show how to adapt these algorithms such that they solve the corresponding problem for graphs with bounded asteroidal number in polynomial time. Finally, we observe that the problems CLIQUE and PARTITION INTO CLIQUES remain NP-complete when restricted to AT-free graphs.