Algebraically Grid-Like Graphs have Large Tree-Width
نویسندگان
چکیده
منابع مشابه
Tree-width and large grid minors in planar graphs
We call H a minor of a graph G if H is obtainable from a subgraph of G by edge contractions. If g ≥ 2, the g-grid is the simple graph with vertices vij (1 ≤ i, j ≤ g) where vij and vi′j′ are adjacent if |i− i′|+ |j − j′| = 1; see Robertson and Seymour (1991). A tree-decomposition of a graph G , is a pair (T, S), where T is a tree and S = {St : t ∈ V (T )} is a family of subsets of V (G), called...
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Probe interval graphs (PIGs) are used as a generalization of interval graphs in physical mapping of DNA.G= (V ,E) is a probe interval graph (PIG) with respect to a partition (P,N) ofV if vertices of G correspond to intervals on a real line and two vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is in P; vertices belonging to P are called pro...
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Given a plane graph G, we wish to draw it in the plane in such a way that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints. An additional objective is to minimize the size of the resulting grid. It is known that each plane graph can be drawn in such a way in an (n 2) x (n 2) grid (for n ~> 3), and that no grid smal...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7691