Author

A. Ahadi

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Preprint Sep 2026

Extremal List Gaps and Inapproximability in Additive Graph Labeling

We study a vertex-labeling analogue of the $1$-$2$-$3$ problem and its list version. For a labeling $\ell:V(G)\to\mathbb N$, let $S_\ell(v)=\sum_{w\in N(v)}\ell(w)$. The additive number $\eta(G)$ is the least $k$ for which there exists $\ell:V(G)\to[k]$ such that $S_\ell(u)\ne S_\ell(v)$ for every $uv\in E(G)$, while t...

A. Ahadi, Sharareh Alipour · 0 citations

Preprint Sep 2026

Remote Matching: Exact-Cardinality Approximation and Tight UGC Hardness

In the unrestricted max--min metric $T$-join problem, one seeks an even terminal set $T$ maximizing the cost of a minimum $T$-join. Iwata and Ravi gave a factor-$3/2$ approximation for this problem. We show that this guarantee is tight under the Unique Games Conjecture: no polynomial-time approximation with factor stri...

A. Ahadi, Morteza Alimi, Sharareh Alipour et al. · 0 citations

Preprint Sep 2026

Multiset Colorings of Random Graphs Across Density Regimes

We show that almost every graph admits a partition of its vertex set into three parts such that no two adjacent vertices have the same number of neighbors in each of the three parts. Equivalently, for $G\sim G(n,1/2)$, $\chi_m(G)\le3$ with high probability, improving the previously known bound of five. Here $\chi_m(G)$...

A. Ahadi, Sharareh Alipour · 0 citations