On edges crossing few other edges in simple topological complete graphs
نویسندگان
چکیده
منابع مشابه
Saturated simple and 2-simple topological graphs with few edges
A simple topological graph is a topological graph in which any two edges have at most one common point, which is either their common endpoint or a proper crossing. More generally, in a k-simple topological graph, every pair of edges has at most k common points of this kind. We construct saturated simple and 2-simple graphs with few edges. These are k-simple graphs in which no further edge can b...
متن کاملDisjoint Edges in Topological Graphs
A topological graph G is a graph drawn in the plane so that its edges are represented by Jordan arcs. G is called simple, if any two edges have at most one point in common. It is shown that the maximum number of edges of a simple topological graph with n vertices and no k pairwise disjoint edges is O (
متن کاملMany disjoint edges in topological graphs
A simple topological graph is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any two of them meet at most once. Using a new tool developed in [12] we show that every simple topological graph on n vertices contains Ω(n 1 2 / √ log n) pairwise disjoint edges. This improves the previous lower bound of Ω(n 1 3 ) by Suk [17] and by Fulek and Ru...
متن کاملColour-critical graphs with few edges
A graph G is called k-critical if G is k-chromatic but every proper subgraph of G has chromatic number at most k 1. In this paper the following result is proved. If G is a k-critical graph (k>~4) on n vertices, then 21E(G)I>(k 1)n ÷ ((k 3)/(k 2 3))n + k 4 where n>~k + 2 and n ~ 2 k 1. This improves earlier bounds established by Dirac (1957) and Gallai (1963). (~) 1998 Elsevier Science B.V. All ...
متن کاملGraph Compositions: Deleting Edges from Complete Graphs
Graph compositions are related to compositions of positive integers and partitions of finite sets, and have applications in electrical networks. This paper provides extensions of a previously known result which states that C(K N ) = B(N) B(N 2), where B(N) represents the N th Bell number and C(K N ) is the complete graph on N vertices with one edge deleted.
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 Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.03.005