## Posts Tagged ‘오수일’

### Suil O (오수일), The second largest eigenvalue and vertex-connectivity in regular graphs

Monday, January 23rd, 2017
The second largest eigenvalue and vertex-connectivity in regular graphs
Suil O (오수일)
Department of Applied Mathematics & Statistics, SUNY Korea, Incheon
2017/2/3 Fri 4PM-5PM
In this talk, for a fixed positive integer d at least 3, we study upper
bounds for the second largest eigenvalue in (an n-vertex) d-regular graph to
guarantee a certain vertex-connectivity.

### Suil O (오수일), Interlacing families and the Hermitian spectral norm of digraphs

Wednesday, April 20th, 2016
Interlacing families and the Hermitian spectral norm of digraphs
Suil O (오수일)
Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada
2016/6/1 Wed 4PM-5PM
Recently, Marcus, Spielman, and Srivastava proved the existence of infinite families of bipartite Ramanujan graphs of every degree at least 3 by using the method of interlacing families of polynomials. In this talk, we apply their method to prove that for any connected graph G, there exists an orientation of G such that the spectral radius of the corresponding Hermitian adjacency matrix is at most that of the universal cover of G.

### Suil O, Spectral radius and fractional matchings in graphs

Thursday, November 20th, 2014
in graphs
Suil O
Georgia State University
2014/12/23 Tuesday 4PM-5PM
Room 1409
A fractional matching of a graph G is a function f giving each edge a number between 0 and 1 so that $$\sum_{e \in \Gamma(v)} f(e) \le 1$$ for each $$v \in V(G)$$, where $$\Gamma(v)$$ is the set of edges incident to v. The fractional matching number of G, written $$\alpha’_*(G)$$, is the maximum of $$\sum_{e \in E(G)} f(e)$$ over all fractional matchings f. Let G be an n-vertex graph with minimum degree d, and let $$\lambda_1(G)$$ be the largest eigenvalue of G. In this talk, we prove that if k is a positive integer and $$\lambda_1(G) < d\sqrt{1+\frac{2k}{n-k}}[/latex], then [latex]\alpha'_*(G) > \frac{n-k}{2}$$.

### Suil O, Finding a spanning Halin subgraph in 3-connected {K_{1,3},P_5}-free graphs

Friday, August 22nd, 2014
Finding a spanning Halin subgraph in 3-connected $$\{K_{1,3},P_5\}$$-free graphs
Suil O
Georgia State University, USA
2014/08/28 *Thursday* 4PM-5PM
Room 1409
A Halin graph is constructed from a plane embedding of a tree whose non-leaf vertices have degree at least 3 by adding a cycle through its leaves in the natural order determined by the embedding. In this talk, we prove that every 3-connected $$\{K_{1,3},P_5\}$$-free graph has a spanning Halin subgraph. This result is best possible in the sense that the statement fails if $$K_{1,3}$$ is replaced by $$K_{1,4}$$ or $$P_5$$ is replaced by $$P_6$$. This is a joint work with Guantao Chen, Jie Han, Songling Shan, and Shoichi Tsuchiya.

### Suil O (오수일), Path Cover Number in 4-regular Graphs and Hamiltonicity in Connected Regular Graphs

Saturday, April 28th, 2012
Path Cover Number in 4-regular Graphs and Hamiltonicity in Connected Regular Graphs
Suil O (오수일)
Department of Mathematics, The College of William and Mary, Williamsburg, Virginia, USA
2012/5/16 Wed 4PM
A path cover of a graph is a set of disjoint paths such that every vertex in the graph appears in one of the paths. We prove an upper bound for the minimum size of a path cover in a connected 4-regular graph with n vertices, confirming a conjecture by Graffiti.pc. We also determine the minimum number of vertices in a connected k-regular graph that is not Hamiltonian, and we solve the analogous problem for Hamiltonian paths.
This is a partly joint work with Gexin Yu and Rui Xu.