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arXiv · 2509.24064

Edge inducibility via local directed graphs

Ting-Wei Chao·Asaf Cohen Antonir·Anqi Li·Hung-Hsun Hans Yu
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Abstract

In this paper we introduce the edge inducibility problem. This is a common refinement of both the well known Kruskal--Katona theorem and the inducibility question introduced by Pippenger and Golumbic. Our first result is a hardness result. It shows that for any graph $G$, there is a related graph $G'$ whose edge inducibility determines the vertex inducibility of $G$. Moreover, we determine the edge inducibility of every $G$ with at most $4$ vertices, and make some progress on the cases $G=C_5,P_6$. Lastly, we extend our hardness result to graphs with a perfect matching that is the unique fractional perfect matching. This is done by introducing locally directed graphs, which are natural generalizations of directed graphs.

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Ting-Wei Chao, Asaf Cohen Antonir, Anqi Li, Hung-Hsun Hans Yu. 2025-09-28. Edge inducibility via local directed graphs. https://arxiv.org/abs/2509.24064

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