combinatorics / Graph theory
Every finite connected simple graph G satisfies $$\alpha(G)\ge r(G)+\ln(\rho(G)),$$ where $\alpha(G)$ is the independence number, $r(G)$ is the radius, and $\rho(G)$ is the minimum number of pairwise vertex-disjoint paths whose vertices cover $V(G)$.
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Infinite family of counterexamples; mathematical argument internally checked, with external verification and novelty review pending.
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Every finite connected simple graph G satisfies $$\alpha(G)\ge r(G)+\ln(\rho(G)),$$ where $\alpha(G)$ is the independence number, $r(G)$ is the radius, and $\rho(G)$ is the minimum number of pairwise vertex-disjoint paths whose vertices cover $V(G)$.
Infinite family of counterexamples; mathematical argument internally checked, with external verification and novelty review pending.
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