منابع مشابه
Planarity and Edge Poset Dimension
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 ...
متن کاملBoxicity 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 کاملDimension-2 poset competition numbers and dimension-2 poset double competition numbers
LetD = (V (D), A(D)) be a digraph. The competition graph ofD, is the graphwith vertex set V (D) and edge set {uv ∈ ( V (D) 2 ) : ∃w ∈ V (D), uw, vw ∈ A(D)}. The double competition graph of D, is the graph with vertex set V (D) and edge set {uv ∈ ( V (D) 2 )
متن کاملPoset edge-labellings and left modularity
It is known that a graded lattice of rank n is supersolvable if and only if it has an EL-labelling where the labels along any maximal chain are exactly the numbers 1, 2, . . . , n without repetition. These labellings are called Sn EL-labellings, and having such a labelling is also equivalent to possessing a maximal chain of left modular elements. In the case of an ungraded lattice, there is a n...
متن کاملOn an extremal problem for poset dimension
Let f(n) be the largest integer such that every poset on n elements has a 2-dimensional subposet on f(n) elements. What is the asymptotics of f(n)? It is easy to see that f(n) > n. We improve the best known upper bound and show f(n) = O(n). For higher dimensions, we show fd(n) = O ( n d d+1 ) , where fd(n) is the largest integer such that every poset on n elements has a d-dimensional subposet o...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1996
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0064