Rank-Width and Well-Quasi-Ordering
نویسندگان
چکیده
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 کاملWell - quasi - ordering versus clique - width ∗
Does well-quasi-ordering by induced subgraphs imply bounded clique-width for hereditary classes? This question was asked by Daligault, Rao and Thomassé in [7]. We answer this question negatively by presenting a hereditary class of graphs of unbounded clique-width which is well-quasi-ordered by the induced subgraph relation. We also show that graphs in our class have at most logarithmic clique-w...
متن کاملRank-width and Well-quasi-ordering of Skew-symmetric Matrices: (extended abstract)
Robertson and Seymour prove that a set of graphs of bounded tree-width is wellquasi-ordered by the graph minor relation. By extending their methods to matroids, Geelen, Gerards, and Whittle prove that a set of matroids representable over a fixed finite field are well-quasi-ordered if it has bounded branch-width. More recently, it is shown that a set of graphs of bounded rank-width (or clique-wi...
متن کاملRank-width and Well-quasi-ordering of Skew-Symmetric or Symmetric Matrices (extended abstract)
We prove that every infinite sequence of skew-symmetric or symmetric matrices M1, M2, . . . over a fixed finite field must have a pair Mi, Mj (i < j) such that Mi is isomorphic to a principal submatrix of the Schur complement of a nonsingular principal submatrix in Mj , if those matrices have bounded rank-width. This generalizes three theorems on well-quasi-ordering of graphs or matroids admitt...
متن کاملBranch-Width and Well-Quasi-Ordering in Matroids and Graphs
We prove that a class of matroids representable over a fixed finite field and with bounded branch-width is well-quasi-ordered under taking minors. With some extra work, the result implies Robertson and Seymour’s result that graphs with bounded tree-width (or equivalently, bounded branch-width) are well-quasi-ordered under taking minors. We will not only derive their result from our result on ma...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2008
ISSN: 0895-4801,1095-7146
DOI: 10.1137/050629616