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
Spectral radius and fractional matchings
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.