Forbidden spiders: A forbidden substructure characterisation of temporal planarity

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• Will Turner (Birmingham)
• Thursday 12 October 2023, 15:00-16:00
• Poynting Small Lecture Theatre (S06).

If you have a question about this talk, please contact Dr. Jan Kurkofka.

Many topoligcal properties of combinatorial objects can be characterised by the forbidden substructures. In this talk we will explore a temporal analogue of planar graphs and prove a forbidden substructure result.

Given a graph $G$, we can obtain a \emph{minor} $H$ of $G$ by deleting and contracting edges from $G$. A \emph{temporal sequence} is a sequence of graphs $(G_1,\ldots,G_n)$ such that $G_i$ is a graph minor of $G_{i+1}$, or $G_{i+1}$ is a graph minor of $G_i$ for each $i\in[n-1]$. A temporal sequence generalises the notion of a temporal graph; indeed, a temporal graph can be thought of as a temporal sequence where the minor operations are only deletions.

Given a temporal sequence $(G)=(G_1,\ldots,G_n)$, we say that a sequence of planar embeddings $I=(\iota_i:G_i\hookrightarrow S^2)$ is a \emph{simultaneous embedding} of $(G)$ if the embeddings are `compatible with respect to the minor relations’. We will investigate when a temporal sequence has a simultaneous embedding.

This will be difficult in general, but we will be able to provide characterisations for some classes of temporal sequence.

This talk is part of the Combinatorics and Probability seminar series.

This talk is included in these lists:

• Combinatorics and Probability seminar
• Poynting Small Lecture Theatre (S06)
• School of Mathematics events

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