# Graph minors and the linear reducibility of Feynman diagrams

@article{Moore2017GraphMA, title={Graph minors and the linear reducibility of Feynman diagrams}, author={Benjamin Moore and Karen A. Yeats}, journal={Advances in Theoretical and Mathematical Physics}, year={2017} }

We look at a graph property called reducibility which is closely related to a condition developed by Brown to evaluate Feynman integrals. We show for graphs with a fixed number of external momenta, that reducibility with respect to both Symanzik polynomials is graph minor closed. We also survey the known forbidden minors and the known structural results. This gives some structural information on those Feynman diagrams which are reducible.

## One Citation

### Some results on double triangle descendants of $K_5$

- MathematicsAnnales de l’Institut Henri Poincaré D
- 2021

Double triangle expansion is an operation on $4$-regular graphs with at least one triangle which replaces a triangle with two triangles in a particular way. We study the class of graphs which can be…

## References

SHOWING 1-10 OF 27 REFERENCES

### Multiple polylogarithms and linearly reducible Feynman graphs

- Mathematics
- 2013

We review an approach for the computation of Feynman integrals by use of multiple polylogarithms, with an emphasis on the related criterion of linear reducibility of the graph. We show that the set…

### Feynman graph polynomials

- Mathematics
- 2010

The integrand of any multiloop integral is characterized after Feynman parametrization by two polynomials. In this review we summarize the properties of these polynomials. Topics covered in this…

### Forbidden minors for graphs with no first obstruction to parametric Feynman integration

- MathematicsDiscret. Math.
- 2015

### The structure of graphs not topologically containing the Wagner graph

- MathematicsJ. Comb. Theory, Ser. B
- 2016

### Quantum periods : A census of φ 4-transcendentals

- Mathematics
- 2010

Perturbative quantum field theories frequently feature rational linear combinations of multiple zeta values (periods). In massless φ4theory we show that the periods originate from certain “primitive”…

### MINORS IN LARGE 6-CONNECTED GRAPHS

- Mathematics
- 2018

Jørgensen conjectured that every 6-connected graph G with no K 6 minor has a vertex whose deletion makes the graph planar. We prove the conjecture for all suﬃciently large graphs.

### The Massless Higher-Loop Two-Point Function

- Mathematics
- 2009

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph G to evaluate to…