Vadim E. Levit

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20242026

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8 papers · 1 filter

math.CO2026

Annihilation, Independence, and Residue: Sharp Matching Bounds for the Annihilation Gap and a TxGraffiti Application

Ohr Kadrawi, Vadim E. Levit

Let $G$ be a finite simple graph. The annihilation number $a (G)$ is an efficiently computable upper bound on the independence number $I^\pm (G)$ . We develop a sharp matching-number the…

math.CO2026

A Ridge-Saturation Characterization of $I^\pm$ -Critical $W_{p}$ Graphs

Do Trong Hoang, Vadim E. Levit, Eugen Mandrescu +1

We characterize the graphs which are simultaneously $I^\pm$ -critical and members of the class $W_{p}$ . The characterization is stated in three equivalent languages. In the graph…

math.CO2026

Graphs with core(G) = nucleus(G)

Vadim E. Levit, Eugen Mandrescu, Kevin Pereyra

Let $G$ be a finite simple graph. An independent set $I$ of $G$ is critical if $∣ I ∣ - ∣ N (I) ∣ \geq ∣ J ∣ - ∣ N (J) ∣$ for every independent set $J$ o…

math.CO2026

The family of all local maximum independent sets is an augmentoid

Vadim E. Levit, Eugen Mandrescu

It was proved in (Levit and Mandrescu, 2022) that both $(V (G), C r o w n (G))$ and $(V (G), C r i t I n d e p (G))$ are augmentoids, established partial augmentation phenomena for the family $Î¨(…

math.CO2026

Closing Trees into Unicyclic Counterexamples

Vadim E. Levit, Ohr Kadrawi

We develop a family-based route to unicyclic graphs whose independence polynomials are unimodal but not log-concave. The paper is organized around one flagship statement: for the e…

math.CO2025

Structural properties and characterizations of $W_{p}$ class

Do Trong Hoang, Vadim E. Levit, Eugen Mandrescu

We establish new characterizations of graphs belonging to the $W_{p}$ class. In addition, we characterize locally triangle-free $I^\pm$ -critical graphs in this class. As a cons…

Annihilation, Independence, and Residue: Sharp Matching Bounds for the Annihilation Gap and a TxGraffiti Application

A Ridge-Saturation Characterization of I^±-Critical Wp​ Graphs

Graphs with core(G) = nucleus(G)

The family of all local maximum independent sets is an augmentoid

Closing Trees into Unicyclic Counterexamples

Structural properties and characterizations of Wp​ class

A Ridge-Saturation Characterization of $I^\pm$ -Critical $W_{p}$ Graphs

Structural properties and characterizations of $W_{p}$ class