منابع مشابه
Box representations of embedded graphs
A d-box is the cartesian product of d intervals of R and a d-box representation of a graph G is a representation of G as the intersection graph of a set of d-boxes in R. It was proved by Thomassen in 1986 that every planar graph has a 3-box representation. In this paper we prove that every graph embedded in a fixed orientable surface, without short non-contractible cycles, has a 5-box represent...
متن کاملGraphs admitting d-realizers: spanning-tree-decompositions and box-representations
A d-realizer is a collection R = {π1, . . . , πd} of d permutations of a set V representing an antichain in R. We use R to define a graph GR on the suspended set V + = V ∪ {s1, . . . , sd}. It turns out that GR has dn+ ( d 2 ) edges (n = |V |), among them the edges of the outer clique on {s1, . . . , sd}. The inner edges of GR can be partitioned into d trees such that Ti spans V + si. In the ca...
متن کاملGraphs admitting d-realizers: tree-decompositions and box-representations
A d-realizer is a collection R = {π1, . . . , πd} of d permutations of a set V representing an antichain in R. We use R to define a graph GR on the suspended set V + = V ∪ {s1, . . . , sd}. It turns out that GR has dn + ( d 2 ) edges (n = |V |), among them the edges of the outer clique on {s1, . . . , sd}. The inner edges of GR can be partitioned into d trees such that Ti spans V + si. In the c...
متن کاملEmbedding Graphs into Embedded Graphs
A drawing of a graph G in the plane is weakly simple if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph G in the plane is weakly simple, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class. In other words, we show that c-planarity with pipes is tractab...
متن کاملSuccinct Representations of Graphs
For a fixed graph property Q, the complexity of the problem: Given a graph G, does G have property Q? is usually investigated as a function of I V I, the number of vertices in G, with the assumption that the input size is polynomial in IV I. In this paper the complexity of these problems is investigated when the input graph is given by a succinct representation. By a succinct representation it ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2016
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-016-9837-8