Rank-width and tree-width of H-minor-free graphs
نویسندگان
چکیده
We prove that for any fixed r ≥ 2, the tree-width of graphs not containing Kr as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph classes such as Kr-minor free graphs and graphs of bounded genus.
منابع مشابه
Rank-Width and Well-Quasi-Ordering
Robertson and Seymour (1990) proved that graphs of bounded tree-width are well-quasi-ordered by the graph minor relation. By extending their arguments, Geelen, Gerards, and Whittle (2002) proved that binary matroids of bounded branch-width are well-quasi-ordered by the matroid minor relation. We prove another theorem of this kind in terms of rank-width and vertex-minors. For a graph G = (V,E) a...
متن کاملGraphs of Small Rank-width Are Pivot-minors of Graphs of Small Tree-width
We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...
متن کاملGraphs of Small Rank-width are Pivot-minors of Graphs of Small Tree-width
We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...
متن کاملLinear rank-width of distance-hereditary graphs II. Vertex-minor obstructions
In the companion paper [Linear rank-width of distance-hereditary graphs I. A polynomialtime algorithm, Algorithmica 78(1):342–377, 2017], we presented a characterization of the linear rank-width of distance-hereditary graphs, from which we derived an algorithm to compute it in polynomial time. In this paper, we investigate structural properties of distance-hereditary graphs based on this charac...
متن کاملGraphs of Bounded Rank-width
We define rank-width of graphs to investigate clique-width. Rank-width is a complexity measure of decomposing a graph in a kind of tree-structure, called a rankdecomposition. We show that graphs have bounded rank-width if and only if they have bounded clique-width. It is unknown how to recognize graphs of clique-width at most k for fixed k > 3 in polynomial time. However, we find an algorithm r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 31 شماره
صفحات -
تاریخ انتشار 2010