Problem 6. Suppose any two odd cycles in a graph \( G \) have a common vertex. Prove \( \chi(G) \leq 5 \) and discuss the equality cases.
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- We are given a graph \( G \) where any two odd cycles share at least one common vertex. - We need to prove that the chromatic number \( \chi(G) \leq 5 \). - We also need to discuss when \( \chi(G) = 5 \). Show more…
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