Author

Antonios Kalampakas

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Preprint Oct 2026

Decomposition Profiles and Weisfeiler-Leman Dimension for Graphs of Bounded Rank Width

The Weisfeiler-Leman (WL) algorithm tests graph isomorphism by assigning colours to $d$-tuples of vertices and iteratively refining the colouring according to neighbourhood configurations until it stabilizes. Increasing $d$ allows the test to detect finer structural differences between graphs, but the computational cos...

Antonios Kalampakas · 0 citations

Preprint Oct 2026

Graphoid Automata, Frobenius PROPs, and Semiring Evaluation

Graphoid automata evaluate graphs by composing relations between words of states. We examine the equations that make this evaluation independent of the chosen graph expression, and what changes when relations are replaced by matrices over a commutative semiring. We prove that the classical graphoid equations are equiva...

Antonios Kalampakas · 0 citations

#edge computing Preprint Sep 2026

Automatic constraints with few subpowers and graphoid recognition

For graphoid automata, these results give polynomial-time recognition without a graph-width restriction, effective boundary composition, and comparison of finite graph relations, and the quadratic boundary bounds are optimal in the worst case.

Antonios Kalampakas · 0 citations

#edge computing Preprint Sep 2026

Width-Bounded Equational Derivations for Finite Graph Expressions

It is proved that equal closed expressions of pattern width at most $k$ are joined by a derivation in which every step applies an equation in either direction and every intermediate width is at most a computable $B_\Sigma(k)$, independently of graph size.

Antonios Kalampakas · 0 citations