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arXiv · 1310.5788

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

Samson Black·Iain Crump·Matt DeVos·Karen Yeats
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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 $Δ-Y$ 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.

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Samson Black, Iain Crump, Matt DeVos, Karen Yeats. 2014-10-02. Forbidden minors for graphs with no first obstruction to parametric Feynman integration. https://arxiv.org/abs/1310.5788

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