Vadim E. Levit

collaborators

9 papers

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.GR2026

Higher Commutativity in Finite Groups, Rigidity, Extremal bounds, and Heisenberg-Type Families

Vadim E Levit, Robert Shwartz

For a finite group $G$ and an integer $r \geq 2$ let $P_{r} (G) := \frac{∣ H o m ( Z ^{r} , G ) ∣}{∣ G ∣ ^{r}},$ where $\Hom(\mathbb Z^r,G)$ is the set of pairwise commuting $r$ -tuples in $G$ .…

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.GR2026

Higher Commutativity in Finite Groups: Exact Asymptotics and Finite Spectrum

Vadim E. Levit, Robert Shwartz

For a finite group G, we study the higher commuting probabilities, namely the probabilities that r randomly chosen elements of G commute pairwise, together with the corresponding n…

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¨(…

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

Higher Commutativity in Finite Groups, Rigidity, Extremal bounds, and Heisenberg-Type Families

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

Higher Commutativity in Finite Groups: Exact Asymptotics and Finite Spectrum

Graphs with core(G) = nucleus(G)

The family of all local maximum independent sets is an augmentoid

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