38 citations · 74 across the 45 of their papers we have counts for
4 papers · 1 filter
Canonization of a random graph by two matrix-vector multiplications
Oleg Verbitsky, Maksim Zhukovskii
We show that a canonical labeling of a random -vertex graph can be obtained by assigning to each vertex the triple , where is the number of…
Tight Bounds on the Asymptotic Descriptive Complexity of Subgraph Isomorphism
Oleg Verbitsky, Maksim Zhukovskii
Let denote the number of vertices in a fixed connected pattern graph . We show an infinite family of patterns such that the existence of a subgraph isomorphic to …
On the First-Order Complexity of Induced Subgraph Isomorphism
Oleg Verbitsky, Maksim Zhukovskii
Given a graph , let be the class of graphs containing as an induced subgraph. Let denote the minimum such that is definable in -variable first-or…
The Descriptive Complexity of Subgraph Isomorphism without Numerics
Oleg Verbitsky, Maksim Zhukovskii
Let be a connected graph with vertices. The existence of a subgraph isomorphic to can be defined in first-order logic with quantifier depth no better than , si…