Ramsey-Type Results for Geometric Graphs, II
نویسندگان
چکیده
منابع مشابه
Ramsey-type Results on Random Graphs
We prove some Ramsey-type theorems, where the colours are replaced by measurable subsets of a probability space. Such results can be also interpreted as percolation problems on N, the complete graph over N, without requiring any specific assumption on the probability, such as independency. In particular, we provide sharp estimates on the probability of finding an infinite clique or an infinite ...
متن کاملRamsey and Turán-type problems in bipartite geometric graphs
A = {(1, 0), (2, 0), . . . , (n, 0)}, B = {((1, 1), (2, 1), . . . , (n, 1)} and the edge ab is the line segment joining a ∈ A and b ∈ B in R. This model is essentially the same as the cyclic bipartite graphs and ordered bipartite graphs considered earlier by several authors. Subgraphs — paths, trees, double stars, matchings — are called non-crossing if they do not contain edges with common inte...
متن کاملDensity theorems for bipartite graphs and related Ramsey-type results
In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new bounds for classical problems in graph Ramsey theory and improve and generalize earlier results of various researchers. The proofs combine probabilistic arguments with some combinatorial ideas. In addition, these techniqu...
متن کاملRamsey-Type Results for Unions of Comparability Graphs
It is well known that the comparability graph of any partially ordered set of n elements contains either a clique or an independent set of size at least pn. In this note we show that any graph of n vertices which is the union of two comparability graphs on the same vertex set, contains either a clique or an independent set of size at least n 13 . On the other hand, there exist such graphs for w...
متن کاملNordhaus-Gaddum type results for the Harary index of graphs
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...
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 & Computational Geometry
سال: 1998
ISSN: 0179-5376
DOI: 10.1007/pl00009391