Christophe Paul

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math.CO2025

The Local Structure Theorem for Graph Minors with finite index

Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos +1

The Local Structure Theorem (LST) for Graph Minors roughly states that for every $H$ -minor-free graph $G$ that contains a sufficiently large wall $W$ , there is a small vertex subse…

math.CO2024

Obstructions to Erdős-Pósa Dualities for Minors

Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos +1

Let $G$ and $H$ be minor-closed graph classes. The pair $(H, G)$ is an Erdős-Pósa pair (EP-pair) if there is a function $f$ where, for every $k$ and ever…

math.CO2024

Delineating Half-Integrality of the Erdős-Pósa Property for Minors: the Case of Surfaces

Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos +1

In 1986 Robertson and Seymour proved a generalization of the seminal result of Erdős and Pósa on the duality of packing and covering cycles: A graph has the Erdős-Pósa property for…