TOPOLOGICAL PROPERTIES OF GRAPHICAL ARRANGEMENTS
نویسندگان
چکیده
منابع مشابه
Topological Complexity of Graphic Arrangements
By combining Yuzvinsky’s criteria from [13] with tools from graph theory, we obtain an explicit combinatorial condition on a finite graph G which guarantees that the higher topological complexity TCs of the complement of the associated graphic arrangement AG is equal to the dimensional upper bound sr − 1, where r is the rank of AG.
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Let G be a simple graph on the vertex set {v1, . . . , vn} with edge set E. Let K be a field. The graphical arrangement AG in K n is the arrangement xi − xj = 0, vivj ∈ E. An arrangement A is supersolvable if the intersection lattice L(c(A)) of the cone c(A) contains a maximal chain of modular elements. The second author has shown that a graphical arrangement AG is supersolvable if and only if ...
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We prove a criterion for k-formality of arrangements, using a complex constructed from vector spaces introduced in [2]. As an application, we give a simple description of k-formality of graphic arrangements: Let G be a connected graph with no loops or multiple edges. Let ∆ be the flag (clique) complex of G and let H•(∆) be the homology of the chain complex of ∆. If AG is the graphic arrangement...
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Let s/* = {l\,li, ■■■ , ln} be a line arrangement in CP2 , i.e., a collection of distinct lines in CP2 . Let L(s/ * ) be the set of all intersections of elements of A* partially ordered byX<Y&YCX.Let M{tf*) be CP2 U-af* where \Jsf* = lj{'i: !<'<"}• The central problem of the theory of arrangement of lines in CP2 is the relationship between M{stf * ) and L{s/*). Main Theorem. The topological typ...
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ژورنال
عنوان ژورنال: Honam Mathematical Journal
سال: 2014
ISSN: 1225-293X
DOI: 10.5831/hmj.2014.36.2.435