17170240
The Z-Transformation graph for an outerplane bipartite graph has a Hamilton path
The Z-transformation graph of perfect matchings of a plane bipartite graph G has the perfect matchings of G as vertices, two perfect matchings being adjacent if their symmetric difference forms a cycle that is the boundary of an interior face of G. In this note, we prove that the Z-transformation graph of perfect matchings of an outerplane bipartite graph has a Hamilton path.
207679368
A Distributive Lattice on the Set of Perfect Matchings of a Plane Bipartite Graph
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.
44874837
Z-transformation graphs of perfect matchings of plane bipartite graphs
Abstract Let G be a plane bipartite graph with at least two perfect matchings. The Z -transformation graph, Z F ( G ), of G with respect to a specific set F of faces is defined as a graph on the perfect matchings of G such that two perfect matchings M 1 and M 2 are adjacent provided M 1 and M 2 differ only in a cycle that is the boundary of a face in F . If F is the set of all interior faces, Z F ( G ) is the usual Z -transformation graph; If F contains all faces of G it is a novel graph and called the total Z -transformation graph. In this paper, we give some simple characterizations for the Z -transformation graphs to be connected by applying the above new idea. Furthermore, we show that the total Z -transformation graph of G is 2-connected if G is elementary; the total Z -transformation digraph of G is strongly connected if and only if G is elementary.
46427487
The Clar Covering Polynomial of Hexagonal Systems I
Abstract In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.
17799789
Cell rotation graphs of strongly connected orientations of plane graphs with an application
The cell rotation graph D(G) on the strongly connected orientations of a 2-edge-connected plane graph G is defined. It is shown that D(G) is a directed forest and every component is an in-tree with one root; if T is a component of D(G), the reversions of all orientations in T induce a component of D(G), denoted by T-, thus (T,T-) is called a pair of in-trees of D(G); G is Eulerian if and only if D(G) has an odd number of components (all Eulerian orientations of G induce the same component of D(G)); the width and height of T are equal to that of T-, respectively. Further it is shown that the pair of directed tree structures on the perfect matchings of a plane elementary bipartite graph G coincide with a pair of in-trees of D(G). Accordingly, such a pair of in-trees on the perfect matchings of any plane bipartite graph have the same width and height.
41201857
A Note on the Number of Perfect Matchings of Bipartite Graphs
Abstract Let G be a bipartite graph with 2n vertices, A its adjacency matrix and K the number of perfect matchings. For plane bipartite graphs each interior face of which is surrounded by a circuit of length 4s + 2, s ϵ {1, 2, …}, an elegant formula, i.e. det A = (−1)nK2, had been rigorously proved by Cvetkovic et al. (1982). For general bipartite graphs, this note contains a necessary and sufficient condition for the above relation to hold. A fast algorithm to check if a plane bipartite graph has such a relation is given.
834526
Efficient 3D reconstruction for face recognition
Face recognition with variant pose, illumination and expression (PIE) is a challenging problem. In this paper, we propose an analysis-by-synthesis framework for face recognition with variant PIE. First, an efficient two-dimensional (2D)-to-three-dimensional (3D) integrated face reconstruction approach is introduced to reconstruct a personalized 3D face model from a single frontal face image with neutral expression and normal illumination. Then, realistic virtual faces with different PIE are synthesized based on the personalized 3D face to characterize the face subspace. Finally, face recognition is conducted based on these representative virtual faces. Compared with other related work, this framework has following advantages: (1) only one single frontal face is required for face recognition, which avoids the burdensome enrollment work; (2) the synthesized face samples provide the capability to conduct recognition under difficult conditions like complex PIE; and (3) compared with other 3D reconstruction approaches, our proposed 2D-to-3D integrated face reconstruction approach is fully automatic and more efficient. The extensive experimental results show that the synthesized virtual faces significantly improve the accuracy of face recognition with changing PIE.
1887353
An Application of Well-Orderly Trees in Graph Drawing
Well-orderly trees seem to have the potential of becoming a powerful technique capable of deriving new results in graph encoding, graph enumeration and graph generation [3, 4]. In this paper, we reduce the height of the visibility representation of plane graphs from 5n/6 to (4n–1)/5, by using well-orderly trees.
39496103
An Application of Well-orderly Trees in Graph Drawing
Well-orderly tree is a powerful technique capable of deriving new results in graph encoding, graph enumeration and graph generation [3, 5]. In this paper, by using well-orderly trees, we prove that any plane graph G with n vertices has a visibility representation with height , which can be constructed in linear time. This improves the best previous bound of .
1857778
Boosting image orientation detection with indoor vs. outdoor classification
Automatic detection of image orientation is a very important operation in photo image management. In this paper, we propose an automated method based on the boosting algorithm to estimate image orientations. The proposed method has the capability of rejecting images based on the confidence score of the orientation detection. Also, images are classified into indoor and outdoor, and this classification result is used to further refine the orientation detection. To select features more sensitive to the rotation, we combine the features by subtraction operation and select the most useful features by boosting algorithm. The proposed method has several advantages: small model size, fast classification speed, and effective rejection scheme.
10720283
Discriminant Analysis on Embedded Manifold
Previous manifold learning algorithms mainly focus on uncovering the low dimensional geometry structure from a set of samples that lie on or nearly on a manifold in an unsupervised manner. However, the representations from unsupervised learning are not always optimal in discriminating capability. In this paper, a novel algorithm is introduced to conduct discriminant analysis in term of the embedded manifold structure. We propose a novel clustering algorithm, called Intra-Cluster Balanced K-Means (ICBKM), which ensures that there are balanced samples for the classes in a cluster; and the local discriminative features for all clusters are simultaneously calculated by following the global Fisher criterion. Compared to the traditional linear/kernel discriminant analysis algorithms, ours has the following characteristics: 1) it is approximately a locally linear yet globally nonlinear discriminant analyzer; 2) it can be considered a special Kernel-DA with geometry-adaptive-kernel, in contrast to traditional KDA whose kernel is independent to the samples; and 3) its computation and memory cost are reduced a great deal compared to traditional KDA, especially for the cases with large number of samples. It does not need to store the original samples for computing the low dimensional representation for new data. The evaluation on toy problem shows that it is effective in deriving discriminative representations for the problem with nonlinear classification hyperplane. When applied to the face recognition problem, it is shown that, compared with LDA and traditional KDA on YALE and PIE databases, the proposed algorithm significantly outperforms LDA and