[Turkmath:7065] Weekly Online Seminar "Analysis and Applied Mathematics"

[Allaberen Ashyralyev]

Dear All,

You are cordially invited to the  Weekly Online Seminar “Analysis and
Applied Mathematics” on

*Date*: Tuesday, March 18, 2025

*Time:* 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)
*Place:* Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09
<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fus02web.zoom.us%2Fj%2F6678270445%3Fpwd%3DSFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09&data=05%7C02%7Callaberen.ashyralyev%40bau.edu.tr%7C2c69a1c488e64e2b9bc708dd55bd50d4%7C8985f9b5679c4a398db6854329895dac%7C0%7C0%7C638760994070534085%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=Gij6wlPSQkpjoR6YOo1LU1YeYpnyd5gzziaGjQgIEDA%3D&reserved=0>,
Conference ID: 667 827 0445, Access code: 1



*Speaker:  Onur Ağırseven Marlboro College, USA(Joint work with Dr. M. A.
Ollis, Emerson College, USA)*

*Title: * On the Buratti-Horak-Rosa conjecture

*Abstract:* Consider the complete graph Kv. Label the vertices with the
distinct elements of Zv, the


cyclic group of order v. Label each edge with the cyclical distance between
its end-vertices. Accord-
ingly, each path in Kv is associated with a multiset of such edge labels.
The Buratti-Horak-Rosa

(BHR) conjecture, initially proposed in 2007 and reformulated several
times, asks the reverse ques-
tion for Hamiltonian paths through Kv. This has certain implications for
graph decompositions, which, in return, have applications in computer
science, including partitioning networks for structural analysis.
In more precise terms, a Hamiltonian path through Kv is called a
realization of a multiset L of
size v − 1 if its edge labels are L. The BHR conjecture is that there is a
realization for a multiset LL if
and only if, for any divisor dd of v, the number of multiples of dd in L is
at most v − d. It has been
shown early on that the conjecture holds for multisets of support at most
2. However, only partial
results have been achieved so far for other supports.
We observe that a toroidal lattice of vertices is associated with a given
multiset. This allows us
to construct certain useful types of realizations as building blocks [1, 2,
3]. Our current focus is mainly on multisets with support of size 3, where
certain relevant lattices are cylindrical. The ongoing expansion of our
constructions is considerably extending the parameters for which the
conjecture is known to hold.

References:

[1] O. Ağırseven and M. A. Ollis, Grid-based graphs, linear realizations
and the Buratti-Horak-
Rosa conjecture, submitted, arXiv:2402.08736.

[2] O. Ağırseven and M. A. Ollis, A coprime Buratti-Horak-Rosa conjecture
and grid-based lin-
ear realizations, submitted, arXiv:2412.05750.

[3] O. Ağırseven and M. A. Ollis, Construction techniques for linear
realizations of multisets with
small support, submitted, arXiv:2502.00164.

 *Abstracts and forthcoming talks can be found on our webpage*

https://sites.google.com/view/aam-seminars
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With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University,**34349**, Istanbul,
Turkiye*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars

https://ejaam.org/editorial.html

*https://icaam-online.org/ <https://icaam-online.org/>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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