combinatorics / Graph theory (automated conjecture)
Let $G$ be a simple connected graph on $n\geq 5$ vertices. If the maximum over all vertices $v$ of $\ell(v)$ - the independence number of the subgraph induced by the open neighborhood $N(v)$ - is at most $1$, must $G$ be well totally dominated? Answered affirmatively; the Lean proof in fact needs only $n\geq 2$, and retains the conjecture's $n\geq 5$ to state the source faithfully.
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The formalization proves the statement under the weaker hypothesis n >= 2; the pull request marking the conjecture solved is open, not merged
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Let $G$ be a simple connected graph on $n\geq 5$ vertices. If the maximum over all vertices $v$ of $\ell(v)$ - the independence number of the subgraph induced by the open neighborhood $N(v)$ - is at most $1$, must $G$ be well totally dominated? Answered affirmatively; the Lean proof in fact needs only $n\geq 2$, and retains the conjecture's $n\geq 5$ to state the source faithfully.
The formalization proves the statement under the weaker hypothesis n >= 2; the pull request marking the conjecture solved is open, not merged
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