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Nanao Kita - One of the best experts on this subject based on the ideXlab platform.

Heping Zhang - One of the best experts on this subject based on the ideXlab platform.

  • the maximum forcing number of cylindrical grid toroidal 4 8 lattice and klein bottle 4 8 lattice
    Journal of Mathematical Chemistry, 2016
    Co-Authors: Xiaoyan Jiang, Heping Zhang
    Abstract:

    Let G be a graph that admits a Perfect matching. A forcing set for a Perfect matching M of G is a subset S of M, such that S is contained in no other Perfect Matchings of G. The smallest cardinality of a forcing set of M is called forced matching number, denoted by f(G, M). Among all Perfect Matchings of G, the maximum forcing matching number is called the maximum forcing number of G, denoted by F(G). In this paper, we show that the maximum forcing numbers of cylindrical grid \(P_{2m}\times C_{2n+1}\) is \(m(n+1)\) by choosing a suitable independent set of this graph. This solves an open problem proposed by Afshani et al. (Australas J Combin 30:147–160, 2004). Moreover, we obtain that the maximum forcing numbers of two classes of toroidal 4–8 lattice and two classes of Klein bottle 4–8 lattice are all equal to the number of squares pq.

  • a distributive lattice on the set of Perfect Matchings of a plane bipartite graph
    Order, 2003
    Co-Authors: Peter Che Bor Lam, Heping Zhang
    Abstract:

    Let G be a plane bipartite graph and M(G) the set of Perfect Matchings of G. The Z-transformation graph of G is defined as a graph on M(G): M,M′∈M(G) are joined by an edge if and only if they differ only in one cycle that is the boundary of an inner face of G. A property that a certain orientation of the Z-transformation graph of G is acyclic implies a partially ordered relation on M(G). An equivalent definition of the poset M(G) is discussed in detail. If G is elementary, the following main results are obtained in this article: the poset M(G) is a finite distributive lattice, and its Hasse diagram is isomorphic to the Z-transformation digraph of G. Further, a distributive lattice structure is established on the set of Perfect Matchings of any plane bipartite graph.

Mccarty Ben - One of the best experts on this subject based on the ideXlab platform.

Persi Diaconis - One of the best experts on this subject based on the ideXlab platform.

Kwan Matthew - One of the best experts on this subject based on the ideXlab platform.

  • Almost all Steiner triple systems have Perfect Matchings
    'Wiley', 2020
    Co-Authors: Kwan Matthew
    Abstract:

    We show that for any n divisible by 3, almost all order-n Steiner triple systems have a Perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of Perfect Matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a uniformly random Steiner triple system to the outcome of the triangle removal process, which we hope will be useful for other problems. Our methods can also be adapted to other types of designs; for example, we sketch a proof of the theorem that almost all Latin squares have transversals

  • Almost all Steiner triple systems are almost resolvable
    'Cambridge University Press (CUP)', 2020
    Co-Authors: Ferber Asaf, Kwan Matthew
    Abstract:

    We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint Perfect Matchings (that is, almost all Steiner triple systems are almost resolvable)