오수일

Archive of posts with tag '오수일'

  • Suil O (오수일), An odd [1,b]-factor in regular graphs from eigenvalues

    IBS/KAIST Joint Discrete Math Seminar

    An odd [1,b]-factor in regular graphs from eigenvalues
    Suil O (오수일)
    Department of Applied Mathematics and Statistics, SUNY-Korea
    2019/06/19 Wed 4:30PM-5:30PM
    An odd [1,b]-factor of a graph is a spanning subgraph H such that for every vertex v∈V(G), 1≤dH(v)≤b, and dH(v) is odd. For positive integers r≥3 and b≤r, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an r-regular graph with even number of vertices to guarantee the existence of an odd [1,b]-factor. In this talk, we improve their bound.
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  • Suil O (오수일), Interlacing families and the Hermitian spectral norm of digraphs
    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.
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  • Suil O, Spectral radius and fractional matchings in graphs
    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}.
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  • Suil O, Finding a spanning Halin subgraph in 3-connected {K_{1,3},P_5}-free graphs
    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.
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  • Suil O (오수일), Path Cover Number in 4-regular Graphs and Hamiltonicity in Connected Regular Graphs
    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.
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  • Suil O (오수일), Usage of Balloons in Regular Graphs
    Usage of Balloons in Regular Graphs
    Suil O (오수일)
    Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
    2011/5/26 Thu 27 Fri 4PM-5PM (Room 3433)
    Petersen proved that every cubic graph without cut-edges has a perfect matching, but some graphs with cut-edges have no perfect matching. The smallest cubic graph with no perfect matching belongs to a general family applicable to many problems on connected d-regular graphs with n vertices. These include the smallest matching number for such graphs and a relationship between the eigenvalues and the matching number. In addition to these results, we present new results involving this family and the Chinese Postman Problem and a relationship between eigenvalues and edge-connectivity in regular graphs.
    This is partly joint work with Sebastian M. Cioaba and Doulgas B. West.
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