The paper proves g(r) ≥ 3r−4 for all r and g(r) ≥ (61/20−o(1))r for large r, answering Erdős's question of whether g(r) can be below 3r.
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An Improved Lower Bound for the Erd\H{o}s-Lov\'asz Cover Number Problem
The paper proves g(r) ≥ 3r−4 for all r and g(r) ≥ (61/20−o(1))r for large r, answering Erdős's question of whether g(r) can be below 3r.