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arXiv · 2308.12190

The Hereditary Closure of the Unigraphs

Michael D. Barrus·Ann N. Trenk·Rebecca Whitman
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Abstract

A graph with degree sequence $\pi$ is a \emph{unigraph} if it is isomorphic to every graph that has degree sequence $\pi$. The class of unigraphs is not hereditary and in this paper we study the related hereditary class HCU, the hereditary closure of unigraphs, consisting of all graphs induced in a unigraph. We characterize the class HCU in multiple ways making use of the tools of a decomposition due to Tyshkevich and a partial order on degree sequences due to Rao. We also provide a new characterization of the class that consists of unigraphs for which all induced subgraphs are also unigraphs.

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Michael D. Barrus, Ann N. Trenk, Rebecca Whitman. 2023-08-23. The Hereditary Closure of the Unigraphs. https://arxiv.org/abs/2308.12190

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