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Discrete Mathematics & Math
Q95 / 100
What is the Lovász theta function and its applications?
Correct! Well done.
Incorrect.
The correct answer is B) A semidefinite programming relaxation sandwiched between the clique number and chromatic number: ω(G) ≤ ϑ(Ḡ) ≤ χ(G) — achieves the Shannon capacity of graphs
B
Correct Answer
A semidefinite programming relaxation sandwiched between the clique number and chromatic number: ω(G) ≤ ϑ(Ḡ) ≤ χ(G) — achieves the Shannon capacity of graphs
Explanation
ϑ(G) (Lovász 1979): computable by SDP in polynomial time. ϑ(C₅) = √5 = Shannon capacity of the pentagonal channel. Separates graph parameters that are NP-hard to compute. Pioneered connection between combinatorics and semidefinite programming.
Progress
95/100