Unavoidable Configurations in Complete Topological Graphs
نویسندگان
چکیده
منابع مشابه
Unavoidable Configurations in Complete Topological Graphs
A topological graph is a graph drawn in the plane so that its vertices are represented by points, and its edges are represented by Jordan curves connecting the corresponding points, with the property that any two curves have at most one point in common. We define two canonical classes of topological complete graphs, and prove that every topological complete graph with n vertices has a canonical...
متن کاملUnavoidable topological minors of infinite graphs
A graph G is loosely-c-connected, or l-c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of l-c-connected infinite graphs that form an unavoidable set among the topological minors of l-c-connected infinite gr...
متن کاملConfigurations with Few Crossings in Topological Graphs
In this paper we study the problem of computing subgraphs of a certain configuration in a given topological graph G such that the number of crossings in the subgraph is minimum. The configurations that we consider are spanning trees, s–t paths, cycles, matchings, and κ-factors for κ ∈ {1, 2}. We show that it is NP-hard to approximate the minimum number of crossings for these configurations with...
متن کاملUnavoidable Multicoloured Families of Configurations
Balogh and Bollobás [Combinatorica 25, 2005] prove that for any k there is a constant f(k) such that any set system with at least f(k) sets reduces to a k-star, an k-costar or an k-chain. They proved f(k) < (2k)2 k . Here we improve it to f(k) < 2ck 2 for some constant c > 0. This is a special case of the following result on the multi-coloured forbidden configurations at 2 colours. Let r be giv...
متن کاملUnavoidable Stars in 3-Graphs
Suppose .F is a collection of 3-subsets of (1,2,..., n). The problem of determining the least integer f(n, k) with the property that if l,FT/ >f(n, k) then .7 contains a k-star (i.e., k 3-sets such that the intersection of any pair of them consists of exactly the same element) is studied. It is proved that, for k odd, f(n, k) = k(k 1) n + P(k-‘) and, for k even,f(n, k) = k(k 3/2) n + F(n + k’).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2003
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-0012-9