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arXiv · 1812.00468

A Harary-Sachs Theorem for Hypergraphs

Gregory J. Clark·Joshua Cooper
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Abstract

We generalize the Harary-Sachs theorem to $k$-uniform hypergraphs: the codegree-$d$ coefficient of the characteristic polynomial of a uniform hypergraph ${\cal H}$ can be expressed as a weighted sum of subgraph counts over certain multi-hypergraphs with $d$ edges. We include a detailed description of the aforementioned multi-hypergraphs and a formula for their corresponding weights.

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Gregory J. Clark, Joshua Cooper. 2021-07-22. A Harary-Sachs Theorem for Hypergraphs. https://arxiv.org/abs/1812.00468

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