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

Samson Black; Iain Crump; Matt DeVos; Karen Yeats

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

Combinatorics 2014-10-06 v2

Authors: Samson Black , Iain Crump , Matt DeVos , Karen Yeats

Abstract

We give a characterization of 3-connected graphs which are planar and forbid cube, octahedron, and $H$ minors, where $H$ is the graph which is one $\Delta-Y$ away from each of the cube and the octahedron. Next we say a graph is Feynman 5-split if no choice of edge ordering gives an obstruction to parametric Feynman integration at the fifth step. The 3-connected Feynman 5-split graphs turn out to be precisely those characterized above. Finally we derive the full list of forbidden minors for Feynman 5-split graphs of any connectivity.

Keywords

graph theory

Cite

@article{arxiv.1310.5788,
  title  = {Forbidden minors for graphs with no first obstruction to parametric Feynman integration},
  author = {Samson Black and Iain Crump and Matt DeVos and Karen Yeats},
  journal= {arXiv preprint arXiv:1310.5788},
  year   = {2014}
}

Comments

A few changes suggested by the referees. 55 pages. Code and output is included with the source

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

Abstract

Keywords

Cite

Comments

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