منابع مشابه
Boxicity and Poset Dimension
Let G be a simple, undirected, finite graph with vertex set V (G) and edge set E(G). A k-dimensional box is a Cartesian product of closed intervals [a1, b1]× [a2, b2]× · · · × [ak, bk]. The boxicity of G, box(G) is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes, i.e. each vertex is mapped to a k-dimensional box and two vertices are adjacent...
متن کاملPoset boxicity of graphs
A t-box representation of a graph encodes each vertex as a box in t-space determined by the (integer) coordinates of its lower and upper corner, such that vertices are adjacent if and only if the corresponding boxes intersect. The boxicity of a graph G is the minimum t for which this can be done; equivalently, it is the minimum t such that G can be expressed as the intersection graph of interva...
متن کاملBoxicity and Separation Dimension
A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H , there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smalle...
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This note explores the relation between the boxicity of undirected graphs and the Ferrers dimension of digraphs.
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Dif ferent areas of discrete mathematics lead to instrinsically dif ferent characterizations of planar graphs . Planarity is expressed in terms of topology , combinatorics , algebra or search trees . More recently , Schnyder’s work has related planarity to partial order theory . Acyclic orientations and associated edge partial orders lead to a new characterization of planar graphs , which also ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100786290