# KPPY 91

Tatsuro Ito, Kim Kijeong, Elena Konstantinova, Ilkyoo Choi

Jan 11, 2019. 11:00am-5:30pm at Hotel Nongshim, Pusan.

Schedule | ||

11:00am - 11:50 |
Tatsuro Ito Anhui University China | After the monumental paper of Terwilliger: |

12pm - 1:25 | Lunch | |

1:30 - 2:20 |
Kim Kijeong Pusan national university | TBA |

2:30 - 3:20 |
Elena Konstantinova Sobolev Institute of Mathematics, Russia | Algebraic approach to hamiltonicity of Cayley graphs |

3:30 - 4:20 |
Ilkyoo Choi Hankuk university of foreign studies | Factor theory of graphs and largest regular subgraphs |

4:30 - 5:20 |
TBA TBA |

## Abstracts

Tatsuro Ito

After the monumental paper of Terwilliger:

After the monumental paper of Terwilliger:

I will discuss what has been done and left to be done after the monumental paper of Terwilliger: The Subconstituent Algebra of an Association scheme I, II, III.

Kim Kijeong

TBA

TBA

TBA

Elena Konstantinova

Algebraic approach to hamiltonicity of Cayley graphs

Algebraic approach to hamiltonicity of Cayley graphs

In this talk we discuss hamiltonian problem on Cayley graphs.
In particular, we present an approach for constructing hamiltonian
cycles in Cayley graphs over the symmetric group. This aproach is based
on cyclic coverings of graphs and algebraic operations with them. This
is joint work with Alexey Medvedev, Universite de Namur, Belgium.

Ilkyoo Choi

Factor theory of graphs and largest regular subgraphs

Factor theory of graphs and largest regular subgraphs

For a graph $G$, let $f_2(G)$ denote the largest number of vertices in a $2$-regular subgraph of $G$.
We determine the minimum of $f_2(G)$ over $3$-regular $n$-vertex simple graphs $G$.
To do this, we prove that every $3$-regular multigraph with exactly $c$ cut-edges has a $2$-regular subgraph that omits at most $\max\{0,\lfloor (c-1)/2\rfloor\}$ vertices.
More generally, every $n$-vertex multigraph with maximum degree $3$ and $m$ edges has a $2$-regular subgraph that omits at most $\max\{0,\lfloor (3n-2m+c-1)/2\rfloor\}$ vertices.
These bounds are sharp; we describe the extremal multigraphs.
This is joint work with R. Kim, A. Kostochka, B. Park, and D. B. West.

TBA