Abstract

The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes are discussed.

Citations

991	Algorithmic Graph Theory and Perfect Graphs - Golumbic - 1980
267	Complexity of finding embeddings in a k-tree - Arnborg, Corneil, et al. - 1987
260	Approximation algorithms for NP-complete problems on planar graphs - Baker - 1994
213	Graph rewriting: An algebraic and logic approach - Courcelle - 1990
183	Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey - Arnborg - 1985
101	The intersection graphs of subtrees in trees are exactly the chordal graphs - Gavril - 1974
69	Graph expressions and graph rewriting - Bauderon, Courcelle - 1987
65	A separator theorem for graphs of bounded genus - Gilbert, Hutchinsom, et al. - 1984
63	An algebraic theory of graph reduction - Arnborg, Courcelle, et al. - 1993
63	Monadic second-order evaluations on tree-decomposable graphs, Theoret - Courcelle, Mosbah - 1993
61	The vertex separation and search number of a graph - Ellis, Sudborough, et al. - 1994
59	Discovering treewidth - Bodlaender - 2005
58	The pathwidth and treewidth of cographs - Bodlaender, Möhring - 1993
57	Automatic generation of lineartime algorithms from predicate calculus descriptions of problems on recursively constructed graph families - Borie, Parker, et al. - 1992
56	Graph searching, path-width, tree-width and related problems (a survey)”, in Reliability of computer and communication networks - Bienstock - 1991
47	Classes of graphs with bounded tree-width - Bodlaender - 1986
43	Characterization and recognition of partial 3-trees - Arnborg, Proskurowski - 1986
41	Approximating treewidth, pathwidth and minimum elimination tree-height - Bodlaender, Gilbert - 1991
35	Quickly excluding a forest - Bienstock, Robertson, et al. - 1991
30	Thilikos, “Fugitive-search games on graphs and related parameters”, Theoret - Dendris, Kirousis, et al. - 1997
25	Forbidden minors characterization of partial 3-trees - Arnborg, Proskurowski, et al. - 1990
22	On the complexity of covering vertices by faces in a planar graph - Bienstock, Monma - 1988
22	A note on hyperedge replacement - Drewes, Kreowski - 1991
20	Nonconstructive advances in polynomial-time complexity - Fellows, Langston - 1987
18	Planar embedding of planar graphs - Dolev, Leighton, et al. - 1984
17	Linear time computation of optimal subgraphs of decomposable graphs - Bern, Lawler, et al.
16	On interval routing schemes and treewidth - Bodlaender, Tan, et al. - 1995
16	A separator theorem for chordal graphs - Gilbert, Rose, et al. - 1984
6	On the cutwidth and topological bandwidth of a tree - Chung - 1985
5	Hyperedge Replacement - Habel
4	decision and the efficiency of polynomial-time algorithms - search - 1989
3	A simple linear-time algorithm for finding path-decompositions of small width. Manuscript - Cattell, Dinneen, et al. - 1994
1	A lower bound on the area of permutation layents - Aggarwal, Klawe, et al. - 1991
1	graphs with bounded treewidth - Planar - 1988
1	disjoint cycles, Int - On - 1994
1	Balanced decompositions for partial k-trees - Borie, Gupta - 1993
1	Borie, Recursively Constructed Graph Families - B - 1988
1	Gorbunov, An estimate of the tree-width of a graph which has not a given planar grid as a minor - Y - 1993