Y. Yavari

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math.CO2026

A Counterexample to Teschner's Bondage-Number Conjecture

Yousof Yavari

For a finite simple graph $G$ with at least one edge, the bondage number $b (G)$ is the least number of edges whose deletion increases the domination number $γ (G)$ . Teschner conject…

math.CO2026

A Proof of the Imbalance Conjecture

James Alexander Schreib, Yousof Yavari

For an edge $uv$ of a finite simple graph $G$ , its imbalance is $∣ d_{G} (u) - d_{G} (v) ∣$ , and the imbalance multiset $M_{G}$ consists of the imbalances of all edges of $G$ . Kozerenko and Sk…