A lower bound on the number of unit distances between the vertices of a convex polygon
✍ Scribed by Herbert Edelsbrunner; Péter Hajnal
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 218 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
If a graph G with cycle rank p contains both spanning trees with rn and with n end-vertices, rn < n, then G has at least 2p spanning trees with k end-vertices for each integer k, rn < k < n. Moreover, the lower bound of 2p is best possible. [ l ] and Schuster [4] independently proved that such span
We present a lower bound on the independence number of arbitrary hypergraphs in terms of the degree vectors. The degree vector of a vertex v is given by d is the number of edges of size m containing v. We define a function f with the property that any hypergraph H = (V, E) satisfies α(H) ≥ v∈V f (d
Caro (1979) and Wei (1981) established a bound on the size of an independent set of a graph as a function of its degrees. In case the degrees of each vertex's neighbors are also known, we establish a lower bound which is tighter for most graphs.