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arXiv · 2601.04169

A Polynomial Kernel for Face Cover on Non-Embedded Planar Graphs

Thekla Hamm·Sukanya Pandey·Krisztina Szilágyi
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Abstract

Given a planar graph, a subset of its vertices called terminals, and $k \in \mathbb{N}$, the Face Cover Number problem asks whether the terminals lie on the boundaries of at most $k$ faces of some embedding of the input graph. When a plane graph is given in the input, the problem is known to have a polynomial kernel~\cite{GarneroST17}. In this paper, we present the first polynomial kernel for Face Cover Number when the input is a planar graph (without a fixed embedding). Our approach overcomes the challenge of not having a predefined set of face boundaries by building a kernel bottom-up on an SPR-tree while preserving the essential properties of the face cover along the way.

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Thekla Hamm, Sukanya Pandey, Krisztina Szilágyi. 2026-01-07. A Polynomial Kernel for Face Cover on Non-Embedded Planar Graphs. https://arxiv.org/abs/2601.04169

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