11228203
k-factor-covered Regular Graphs
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.
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.
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.
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.
5976625
Augmenting naive Bayes for ranking
Naive Bayes is an effective and efficient learning algorithm in classification. In many applications, however, an accurate ranking of instances based on the class probability is more desirable. Unfortunately, naive Bayes has been found to produce poor probability estimates. Numerous techniques have been proposed to extend naive Bayes for better classification accuracy, of which selective Bayesian classifiers (SBC) (Langley & Sage, 1994), tree-augmented naive Bayes (TAN) (Friedman et al., 1997), NBTree (Kohavi, 1996), boosted naive Bayes (Elkan, 1997), and AODE (Webb et al., 2005) achieve remarkable improvement over naive Bayes in terms of classification accuracy. An interesting question is: Do these techniques also produce accurate ranking? In this paper, we first conduct a systematic experimental study on their efficacy for ranking. Then, we propose a new approach to augmenting naive Bayes for generating accurate ranking, called hidden naive Bayes (HNB). In an HNB, a hidden parent is created for each attribute to represent the influences from all other attributes, and thus a more accurate ranking is expected. HNB inherits the structural simplicity of naive Bayes and can be easily learned without structure learning. Our experiments show that HNB outperforms naive Bayes, SBC, boosted naive Bayes, NBTree, and TAN significantly, and performs slightly better than AODE in ranking.
18261046
Shelling Algorithm in Solid Modeling
Shelling is a powerful modeling operation in current CAD /CAM systems. In this paper, we present a new shelling algorithm for regular B-Rep solids. We first generate an initial offset solid, then correct the self-intersecting offset solid if necessary. We obtain the resultant shelling solid through a regularized Boolean operation finally. The algorithm has been implemented in a solid modeling system, and some examples are given to illustrate it.
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.
14763506
Real-time voxelization for complex polygonal models
In this paper, we present an efficient voxelization algorithm for complex polygonal models by exploiting newest programmable graphics hardware. We first convert the model into three discrete voxel spaces according to its surface orientation. The resultant voxels are encoded as 2D textures and stored in three intermediate sheet buffers called directional sheet buffers. These buffers are finally synthesized into one worksheet, which records the volumetric representation of the target. The whole algorithm traverses the geometric model only once and is accomplished entirely in GPU (graphics processing unit), achieving real-time frame rate for models with up to 2 million triangles.
10673582
Automatic 3D reconstruction for face recognition
An analysis-by-synthesis framework for face recognition with variant pose, illumination and expression (PIE) is proposed in this paper. First, an efficient 2D-to-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 works, this framework has the 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) the 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 variant PIE.