KPPY 60
Alexander Stoimenow, Hemanshu Kaul, Semin Oh, Ojoung Kwon
Nov. 09, 2013. 11:30am5:30pm at KNU
Schedule  
11:00am  11:50 
Alexander Stoimenow Keimyung University  On dual triangulations of surfaces 
12pm  1:25  Lunch  
1:30  2:20 
Hemanshu Kaul Illinois Institute of Technology  Finding Large Subgraphs 
2:30  3:20 
Semin Oh Pusan National University  The number of ideals of $\mathbb{Z}[x]/(x^34x)$ with the given index. 
3:30  4:20 
Ojoung Kwon KAIST  Treelike structure of distancehereditary graphs 
4:30  5:20 

Abstracts
Alexander Stoimenow
On dual triangulations of surfaces
On dual triangulations of surfaces
The goal is to report on some longterm work on certain
combinatorial properties of knot/link diagrams of given
canonical genus. These turned out to have various ramifications
and applications, including (1) enumeration of alternating knots
by genus, (2) words in formal alphabets (Wicks forms), (3) graph
embedding problems on surfaces, (4) markings and the $sl_N$ graph
polynomial, (5) hyperbolic volume of polyhedra, graphs and links.
I will try to explain (at least as far as time allows) some
interrelations between these topics.
Hemanshu Kaul
Finding Large Subgraphs
Finding Large Subgraphs
The maximum subgraph problem for a fixed graph property $P$ asks: Given a graph $G$, find a subgraph $H$ of $G$ that satisfies property $P$ that has the maximum number of edges. Similarly, we can talk about maximum induced subgraph problem. The property $P$ can be planarity, acyclicity, bipartiteness, etc.
We will discuss some old and new problems of this flavor, focusing on the algorithmic aspects of these problems. In particular, we will describe some old results on the maximum bipartite subgraph problem and some new results on the maximum seriesparallel subgraph problem.
Semin Oh
The number of ideals of $\mathbb{Z}[x]/(x^34x)$ with the given index.
The number of ideals of $\mathbb{Z}[x]/(x^34x)$ with the given index.
Let $L$ be the ring $\mathbb{Z}[x]/(x^34x)$. Let $G$ be the quadrangle graph and let $A_G$ be the adjacency matrix of $G$. Then $x^34x$ is the minimal polynomial of $A_G$. Thus $L$ is the ring related to $G$.
Let $\Lambda$ be the subring of $\mathbb{Q}[x]/(x^34x)$ satisfying $\Lambda$ is isomorphic to $L$. In this talk, our aim is to obtain the Dirichlet series of the number of $\Lambda$submodules of $L$. We applied Louis Solomon's works to this calculation by using computer program GAP. We will introduce how to calculate the Dirichlet series.
Ojoung Kwon
Treelike structure of distancehereditary graphs
Treelike structure of distancehereditary graphs
In this talk, we will discuss distancehereditary graphs.
Distancehereditary graphs are exactly the graphs
preserving the distance between two vertices when taking any connected induced subgraph.
There are many characterizations of distancehereditary graphs, one being that they have treelike structure with respect to a certain "split" operation. However, there are few known theorems using this structure.
We provide the following, using the treelike structure of distancehereditary graphs.
1. A characterization of distancehereditary graphs having linear rankwidth at most k.
2. Two variants of Bouchet's Tree Theorem to cographs and diamondfree chordal graphs.
3. A test of local equivalent in distancehereditary graphs.
This is joint work with Mamadou Kante and Isolde Idler.