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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Fabio will not speak about his life, but he will speak about<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
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<b><span style="font-size:11.5pt;font-family:Helvetica;color:black;mso-ligatures:none;mso-fareast-language:EN-GB">Cellular embeddings of levelled spatial graphs<o:p></o:p></span></b></p>
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<span style="font-size:9.0pt;font-family:Helvetica;color:black;mso-ligatures:none;mso-fareast-language:EN-GB">Abstract: Every abstract graph can be embedded on a closed oriented surface and the genus range for the surface is known. If, instead of an abstract
graph, an embedding of a graph is considered, it is still easy to find a closed oriented surface on which the spatial graph is embedded on by placing the graph on the boundary of a tubular neighbourhood of the graph. But in general there is no good control
over the complement of the graph in a surface, it could be a union of discs with any number of punctures. We are interested in finding surfaces for a spatial graph, such that the complement of the graph in the surface is a set of open discs, so called cellular
embeddings. To this end, we introduce a new family of spatial graphs, called levelled embeddings. The defining feature of levelled embeddings is their decomposition into planar subgraphs, all of which are interconnected through a common cycle within the graph.
This structure allows for a systematic exploration of their embedding possibilities. We prove that levelled embeddings of low complexity can always be cellular embedded. We extend this result in a sufficient condition for finding cellular embeddings of levelled
graphs with arbitrarily high complexity.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Party starts at 11:00 in Maryam.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">See you there!<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Thomas<o:p></o:p></span></p>
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