One of these numbers with indices (5, 5) is currently bounded between 43 and 48. For 10 points each:
[10h] Give these numbers named after an American mathematician. For indices m and n, this number is the smallest size of a two-colored complete graph such that there is always a monochromatic complete graph of size m or n.
ANSWER: Ramsey numbers
[10e] Ramsey theory is used to analyze social networks to determine how many people must know each other, with each relationship represented by coloring one of these things. These entities connect vertices on a graph.
ANSWER: edges [accept links or lines]
[10m] This “wandering” mathematician quipped that if aliens demanded the Ramsey number (6, 6), then humans should attack. His namesake “number” counts an author’s separation from him by collaboration on math papers.
ANSWER: Paul Erdős [or Erdős Pál; accept Erdős number]
<KP, Other Science - Math>