Fan Chung and Ron Graham (J. Combin. Theory Ser. B 65 (1995), 273-290) introduced the cover polynomial for a directed graph and showed that it was connected with classical rook theory. M. Dworkin (J. Combin. Theory Ser. B 71 (1997), 17-53) showed that the cover polynomial naturally factors for directed graphs associated with Ferrers boards. The authors (Adv. Appl. Math. 27 (2001), 438-481) deve...

We present an enhanced principal component analysis (PCA) algorithm for improving rate of face recognition. The proposed pre-processing method, termed as perfect histogram matching, modifies the image histogram to match a Gaussian shaped tonal distribution in the face images such that spatially the entire set of face images presents similar facial gray-level intensities while the face content i...

Let G be a matching-covered graph, i.e., every edge is contained in a perfect matching. An edge subsetX ofG is feasible if there exists two perfect matchingsM1 andM2 such that |M1∩X| 6≡ |M2∩X| (mod 2). Lukot’ka and Rollová proved that an edge subset X of a regular bipartite graph is not feasible if and only if X is switching-equivalent to ∅, and they further ask whether a non-feasible set of a ...

Is perfect matching in NC? That is to say, is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in theoretical computer science for over three decades, ever since the discovery of RNC matching algorithms. Within this question, the case of planar graphs has remained an enigma: On the one hand, counting the number of perfect matchings is far harder t...

Consider a planar graph G = (V,E) with polynomially bounded edge weight function w : E → [0, poly(n)]. The main results of this paper are NC algorithms for the following problems: • minimum weight perfect matching in G, • maximum cardinality and maximum weight matching in G when G is bipartite, • maximum multiple-source multiple-sink flow in G where c : E → [1, poly(n)] is a polynomially bounde...

For an arbitrary hypergraph H, let PM(H) be the propositional formula asserting that H contains a perfect matching. We show that every resolution refutation of PM(H) must have size exp ( Ω ( δ(H) λ(H)r(H)(log n(H))(r(H) + log n(H)) )) , where n(H) is the number of vertices, δ(H) is the minimal degree of a vertex, r(H) is the maximal size of an edge, and λ(H) is the maximal number of edges incid...