## Posts Tagged ‘노유미’

### 1st Korean Workshop on Graph Theory

Tuesday, July 28th, 2015
1st Korean Workshop on Graph Theory
August 26-28, 2015
KAIST  (E6-1 1501 & 3435)
http://home.kias.re.kr/MKG/h/KWGT2015/
• Program Book
• Currently, we are planning to have talks in KOREAN.
• Students/postdocs may get the support for the accommodation. (Hotel Interciti)
• Others may contact us if you wish to book a hotel at a pre-negotiated price. Please see the website.
• PLEASE REGISTER UNTIL AUGUST 16.
Location: KAIST
• Room 1501 of E6-1 (August 26, 27)
• Room 3435 of E6-1 (August 28)
Invited Speakers:
Organizers:

### Yoomi Rho (노유미), L(j,k) Labelings of Direct Product of Complete Graphs

Tuesday, March 8th, 2011
L(j,k) labelings of direct product of complete graphs
Yoomi Rho (노유미)
Dept. of Mathematics, Univ. of Incheon, Incheon, Korea.
2011/3/17 Thu 4:30PM-5:30PM (E6-1, Room 3433)
An L(j,k) labeling of a graph is a vertex labeling such that the difference of the labels of any two adjacent vertices is at least j and that of any two vertices of distance 2 is at least k. The minimum of the spans of all L(j,k)-labelings of G is denoted by $$\lambda_k^j(G)$$. Recently Haque and Jha proved if G is a direct product of complete graphs, then $$\lambda_k^j(G)$$ coincide with the trivial lower bound $(N-1)k$ where N is the order of G when j/k is within a certain bound.

In this paper, we suggest a new labeling method of such a graph G. With this method, we extend the range of j/k such that $$\lambda_k^j(G)=(N-1)k$$ holds. Moreover, we obtain an upper bound of $$\lambda_k^j(G)$$ for the remaining cases.

### Yoomi Rho (노유미), Turán type problems forbidding complete graphs and complete multipartite graphs together

Monday, November 10th, 2008
Turán type problems forbidding complete graphs and complete multipartite graphs together
Yoomi Rho (노유미)
Dept. of Mathematics, Univ. of Incheon, Incheon, Korea.
2008/11/28 Fri, 4PM-5PM
A Turán type problem looks for the maximum number of edges of a graph of a given order that does not contain given forms of graphs as subgraphs. These given forms of subgraphs are called the forbidden graphs of the problem. This problem also looks for the forms of graphs which have the maximum number of edges. This line of research is started by Turán who solved the problem forbidding complete graphs in 1941. Problems forbidding complete bipartite graphs or even cycles have been considered. Also there are asymptotic results on problems forbidding complete multipartite graphs. In 1994, Brualdi and Mellendorf raised the following problem which forbids a complete graph and a complete bipartite graph together.

Let t and n be positive integers with n≥t≥2. Determine the maximum number of edges of a graph of order n that contains neither Kt nor Kt,t as a subgraph.

They also solved this problem when n=2t. Obviously when n<2t, the problem reduces to Turán's problem which forbids only Kt. We solve the problem when n=2t+1. We raise a problem which forbids Kt and Kt,n-t together and a problem which forbids Kt and Kt,t,t together.