Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
A characterization of graphs without long induced paths
Journal of Graph Theory
Domination in convex and chordal bipartite graphs
Information Processing Letters
Treewidth for graphs with small chordality
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
New results on induced matchings
Discrete Applied Mathematics
Independent domination in finitely defined classes of graphs
Theoretical Computer Science
On linear and circular structure of (claw, net)-free graphs
Discrete Applied Mathematics
Some results on graphs without long induced paths
Information Processing Letters
On the Band-, Tree-, and Clique-Width of Graphs with Bounded Vertex Degree
SIAM Journal on Discrete Mathematics
NP-hard graph problems and boundary classes of graphs
Theoretical Computer Science
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
On the diameter of i-center in a graph without long induced paths
Journal of Graph Theory
Pathwidth and searching in parameterized threshold graphs
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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It is well known that boundedness of tree-width implies polynomial-time solvability of many algorithmic graph problems. The converse statement is generally not true, i.e., polynomial-time solvability does not necessarily imply boundedness of tree-width. However, in graphs of bounded vertex degree, for some problems, the two concepts behave in a more consistent way. In the present paper, we study this phenomenon with respect to three important graph problems - dominating set, independent dominating set and induced matching - and obtain several results toward revealing the equivalency between boundedness of the tree-width and polynomial-time solvability of these problems in bounded degree graphs.