# Paul Erdős

Paul Erdős was a person.

**Context:**- He has Erdős Number of 0.

**See:**Mathematician, Random Graph, Erdős–Rényi Model.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Paul_Erdős Retrieved:2014-11-3.
**Paul Erdős**(26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians of the 20th century, but also known for his social practice of mathematics (more than 500 collaborators) and eccentric lifestyle (Time Magazine called him*The Oddball's Oddball*). Erdős pursued problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory.^{[1]}

### 1989

- (Erdös et al., 1989) ⇒ Paul Erdős, Pavol Hell and Peter Winkler. (1989). “Bandwidth Versus Bandsize.” In: Annals of Discrete Math. doi:10.1016/S0167-5060(08)70455-2
- QUOTE: The bandwidth (bandsize) of a graph G is the minimum, over all bijections u: V(G) → {1,2,…,|V(G)|}, of the greatest difference (respectively the number of distinct differences) |u(v) — u(w)| for vw ɛE(G).
We show that a graph on n vertices with bandsize k has bandwidth between k and cn1-1/n, and that this is best possible. In the process we obtain best possible asymptotic bounds on the bandwidth of circulant graphs.

The bandwidth and bandsize of random graphs are also compared, the former turning out to be n — C1 log n and the latter at least n — c2 (logn)2.

- QUOTE: The bandwidth (bandsize) of a graph G is the minimum, over all bijections u: V(G) → {1,2,…,|V(G)|}, of the greatest difference (respectively the number of distinct differences) |u(v) — u(w)| for vw ɛE(G).

### 1976

- (Bollobás & Erdős, 1976) ⇒ Béla Bollobás, and Paul Erdős. (1976). “Cliques in Random Graphs.” In: Mathematical Proceedings of the Cambridge Philosophical Society, 80(03).

### 1960

- (Erdős & Rényi, 1960) ⇒ Paul Erdős, and A. Rényi (1960). “On the evolution of random graphs". Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5.

### 1951

- (Erdős & Shapiro, 1951) ⇒ Paul Erdős, and Harold N. Shapiro. (1951). “On the changes of sign of a certain error function."

### 1935

- (Erdős & Szekeres, 1951) ⇒ Paul Erdös, and George Szekeres. (1935). “A Combinatorial Problem in Geometry.” In: Compositio Mathematica, 2.