Page 309 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 309
GRAPHS, POLYNOMIALS, SURFACES, AND KNOTS (MS-49)
Limits for embedding distributions
Yichao Chen, ycchen@hnu.edu.cn
SuZhou University of Science and Technolgy, China
In this paper, we first establish a central limit theorem which is new in probability, then we
find and prove that, under some conditions, the embedding distributions of H-linear family of
graphs with spiders are asymptotic normal distributions. As corollaries, the asymptotic normal-
ity for the embedding distributions of path-like sequence of graphs with spiders and the genus
distributions of ladder-like sequence of graphs are given. We also prove that the limit of Euler-
genus distributions is the same as that of crosscap-number distributions. The results here can
been seen a version of central limit theorem in topological graph theory.
On the Gross-Mansour-Tucker conjecture
Sergei Chmutov, chmutov.1@osu.edu
The Ohio State University, United States
In this presentation I will explain a proof of the Gross, Mansour, Tucker conjecture claiming that
any ribbon graph, distinct from explicit family of special exceptions, has a partial dual graph
of different genus. This is a joint work with Fabien Vignes-Tourneret based of the preprint
arXiv:2101.09319v1 [math.CO].
Embedded graphs and delta-matroids
Carolyn Chun, chun@usna.edu
USNA, United States
Coauthors: Joseph Bonin, Steven Noble, Ralf Rueckriemen, Iain Moffatt, Deboarh Chun
The interplay between embedded graphs and delta-matroids generates useful tools for both
research areas. In this talk we explore such results and propose further applications.
Embeddings with Eulerian faces II: degree conditions
Mark Ellingham, mark.ellingham@vanderbilt.edu
Vanderbilt University, United States
Coauthor: Joanna Ellis-Monaghan
As a natural special case of edge-outer embeddability, we consider the problem of finding max-
imum genus orientable directed embeddings. We allow some faces to be specified in advance.
Digraphs with directed embeddings are necessarily eulerian. If we are given an eulerian digraph
and a decomposition of the arcs into edge-disjoint directed walks, then we can regard this as a
partial embedding, with the walks as specified face boundaries. If we can complete this to an
embedding by adding one more face bounded by an euler circuit, then the embedding will have
maximum genus subject to containing the specified faces. We show that this is always possi-
ble provided the underlying simple graph of our n-vertex digraph has minimum degree at least
307
Limits for embedding distributions
Yichao Chen, ycchen@hnu.edu.cn
SuZhou University of Science and Technolgy, China
In this paper, we first establish a central limit theorem which is new in probability, then we
find and prove that, under some conditions, the embedding distributions of H-linear family of
graphs with spiders are asymptotic normal distributions. As corollaries, the asymptotic normal-
ity for the embedding distributions of path-like sequence of graphs with spiders and the genus
distributions of ladder-like sequence of graphs are given. We also prove that the limit of Euler-
genus distributions is the same as that of crosscap-number distributions. The results here can
been seen a version of central limit theorem in topological graph theory.
On the Gross-Mansour-Tucker conjecture
Sergei Chmutov, chmutov.1@osu.edu
The Ohio State University, United States
In this presentation I will explain a proof of the Gross, Mansour, Tucker conjecture claiming that
any ribbon graph, distinct from explicit family of special exceptions, has a partial dual graph
of different genus. This is a joint work with Fabien Vignes-Tourneret based of the preprint
arXiv:2101.09319v1 [math.CO].
Embedded graphs and delta-matroids
Carolyn Chun, chun@usna.edu
USNA, United States
Coauthors: Joseph Bonin, Steven Noble, Ralf Rueckriemen, Iain Moffatt, Deboarh Chun
The interplay between embedded graphs and delta-matroids generates useful tools for both
research areas. In this talk we explore such results and propose further applications.
Embeddings with Eulerian faces II: degree conditions
Mark Ellingham, mark.ellingham@vanderbilt.edu
Vanderbilt University, United States
Coauthor: Joanna Ellis-Monaghan
As a natural special case of edge-outer embeddability, we consider the problem of finding max-
imum genus orientable directed embeddings. We allow some faces to be specified in advance.
Digraphs with directed embeddings are necessarily eulerian. If we are given an eulerian digraph
and a decomposition of the arcs into edge-disjoint directed walks, then we can regard this as a
partial embedding, with the walks as specified face boundaries. If we can complete this to an
embedding by adding one more face bounded by an euler circuit, then the embedding will have
maximum genus subject to containing the specified faces. We show that this is always possi-
ble provided the underlying simple graph of our n-vertex digraph has minimum degree at least
307
