What the study found
The authors define a tensor product for graphs embedded in pseudo-surfaces and use it to generalize and unify several existing tensor product formulas. They provide Brylawski-style formulas for both the Bollobás-Riordan polynomial and the Krushkal polynomial.
Why the authors say this matters
The study suggests that this framework brings together previously known results for related graph polynomials into a single setting. The authors conclude that it extends the reach of tensor product formulas beyond earlier special cases.
What the researchers tested
The researchers worked with graphs embedded in pseudo-surfaces and defined a tensor product operation for them. They then used this construction to derive formulas relating the polynomials of the tensor product to those of the tensor factors.
What worked and what didn't
The abstract states that the approach succeeds in generalizing and unifying the known tensor product formulas. It also says that Brylawski-style formulas are obtained for the Bollobás-Riordan and Krushkal polynomials, while noting that earlier formulas had only been known in special cases for the Bollobás-Riordan polynomial.
What to keep in mind
The abstract does not describe any limitations, failed cases, or scope restrictions beyond the fact that earlier Bollobás-Riordan results were only available in some special cases.
Key points
- A tensor product is defined for graphs embedded in pseudo-surfaces.
- The construction generalizes and unifies several known tensor product formulas.
- Brylawski-style formulas are given for the Bollobás-Riordan polynomial and the Krushkal polynomial.
- Earlier tensor product formulas for the Bollobás-Riordan polynomial were known only in special cases.
- The abstract does not list specific limitations of the new framework.
Disclosure
- Research title:
- Tensor product formulas extend to two graph polynomials
- Authors:
- Iain Moffatt, Maya Thompson
- Institutions:
- Royal Holloway University of London
- Publication date:
- 2026-04-23
- DOI:
- 10.37236/14206
- OpenAlex record:
- View
- Image credit:
- Photo by Sergey Meshkov on Pexels · Pexels License
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