Stability in circular arc graphs
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Problems and results in combinatorial analysis and graph theory
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Induced matchings in bipartite graphs
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Induced matchings in cubic graphs
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Irredundancy in circular arc graphs
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Modular decomposition and transitive orientation
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New results on induced matchings
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Linear Time Algorithms for Hamiltonian Problems on (Claw,Net)-Free Graphs
SIAM Journal on Computing
Independent Sets in Asteroidal Triple-Free Graphs
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Linear time maximum induced matching algorithm for trees
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Finding a maximum induced matching in weakly chordal graphs
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On linear and circular structure of (claw, net)-free graphs
Discrete Applied Mathematics
Bipartite Domination and Simultaneous Matroid Covers
SIAM Journal on Discrete Mathematics
Induced matchings in asteroidal triple-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
On clique separators, nearly chordal graphs, and the Maximum Weight Stable Set Problem
Theoretical Computer Science
IEEE Journal on Selected Areas in Communications
New min-max theorems for weakly chordal and dually hordal graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
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For a finite undirected graph G = (V ,E ) and positive integer k *** 1, an edge set M *** E is a distance-k matching if the mutual distance of edges in M is at least k in G . For k = 1, this gives the usual notion of matching in graphs, and for general k *** 1, distance-k matchings were called k-separated matchings by Stockmeyer and Vazirani. The special case k = 2 has been studied under the names induced matching (i.e., a matching which forms an induced subgraph in G ) by Cameron and strong matching by Golumbic and Laskar in various papers. Finding a maximum induced matching is $\mathbb{NP}$-complete even on very restricted bipartite graphs but for k = 2, it can be done efficiently on various classes of graphs such as chordal graphs, based on the fact that an induced matching in G corresponds to an independent vertex set in the square L (G )2 of the line graph L (G ) of G which, by a result of Cameron, is chordal for any chordal graph G . We show that, unlike for k = 2, for a chordal graph G , L (G )3 is not necessarily chordal, and finding a maximum distance-3 matching remains $\mathbb{NP}$-complete on chordal graphs. For strongly chordal graphs and interval graphs, however, the maximum distance-3 matching problem can be solved in polynomial time. Moreover, we obtain various new results for induced matchings.