What the study found
The authors define a tensor product of graphs embedded in pseudo-surfaces, which are surface-like spaces that may include nonstandard local structure. Using this definition, they generalize and unify existing tensor product formulas and provide Brylawski-style formulas for the Bollobás-Riordan polynomial and the Krushkal polynomial.
Why the authors say this matters
The study suggests that a single framework can cover several previously known tensor product formulas for graph polynomials. The authors present this as a way to unify results for graph invariants associated with graphs embedded in surfaces and pseudo-surfaces.
What the researchers tested
The researchers developed a tensor product construction for graphs embedded in pseudo-surfaces. They then used this construction to extend formula patterns originally known from Brylawski's tensor product formula for the Tutte polynomial and related results for ribbon graph polynomials and transition polynomials.
What worked and what didn't
The abstract says the new construction succeeds in producing Brylawski-style tensor product formulas for both the Bollobás-Riordan polynomial and the Krushkal polynomial. It also states that the approach generalizes and unifies earlier formulas, including some special-case results for the Bollobás-Riordan polynomial.
What to keep in mind
The abstract does not describe any experimental limitations or unresolved cases. It also does not provide details about proofs, examples, or the scope of the formulas beyond the polynomials named in the summary.
Key points
- A tensor product construction is defined for graphs embedded in pseudo-surfaces.
- The construction is used to generalize and unify known tensor product formulas.
- Brylawski-style formulas are provided for the Bollobás-Riordan polynomial and the Krushkal polynomial.
- The abstract connects the new results to the Tutte polynomial, ribbon graph polynomial, and transition polynomials.
- No specific limitations or caveats are described in the abstract.
Disclosure
- Research title:
- Tensor product formulas are extended to Bollobás-Riordan and Krushkal polynomials
- Authors:
- Iain Moffatt, Maya Thompson
- Institutions:
- Royal Holloway University of London, Royal Holloway University of London
- Publication date:
- 2026-04-23
- DOI:
- 10.37236/14206
- OpenAlex record:
- View
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