Every Graph Is an Integral Distance Graph in the Plane
نویسندگان
چکیده
منابع مشابه
Every Graph Is an Integral Distance Graph in the Plane
We prove that every nite simple graph can be drawn in the plane so that any two vertices have an integral distance if and only if they are adjacent. The proof is constructive.
متن کاملThe Odd-Distance Plane Graph
The vertices of the odd-distance graph are the points of the plane R. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chromatic number of this graph is at least five. We also prove that the odd-distance graph in R is countably choosable, while such a graph in R is not.
متن کاملDifferent-Distance Sets in a Graph
A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...
متن کاملEvery Monotone 3-Graph Property is Testable
Let k ≥ 2 be a fixed integer and P be a property of k-uniform hypergraphs. In other words, P is a (typically infinite) family of k-uniform hypergraphs and we say a given hypergraph H satisfies P if H ∈ P . For a given constant η > 0 a k-uniform hypergraph H on n vertices is η-far from P if no hypergraph obtained from H by changing (adding or deleting) at most ηn edges in H satisfies P . More pr...
متن کاملEvery Graph is a Self - Similar Set
In this paper we prove that every graph (in particular S1) is a selfsimilar space and that [0, 1] is a self-similar set that is not the product of topological spaces, answering two questions posed by C. Ruiz and S. Sabogal in [6].
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: Journal of Combinatorial Theory, Series A
سال: 1997
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2826