44902530
The 2-dipath chromatic number of Halin graphs
26709203
The Linear 2-Arboricity of Outerplanar Graphs
41218825
Relaxed game chromatic number of graphs
This paper discusses a coloring game on graphs. Let k, d be non-negative integers and C a set of k colors. Two persons, Alice and Bob, alternately color the vertices of G with colors from C, with Alice having the first move. A color i is legal for an uncolored vertex x if by coloring x with color i, the subgraph of G induced by those vertices of color i has maximum degree at most d. Each move of Alice or Bob colors an uncolored vertex with a legal color. The game is over if either all vertices are colored, or no more vertices can be colored with a legal color. Alice's goal is to produce a legal coloring which colors all the vertices of G, and Bob's goal is to prevent this from happening. We shall prove that if G is a forest, then for k = 3, d ≥ 1, Alice has a winning strategy. If G is an outerplanar graph, then for k = 6 and d ≥ 1, Alice has a winning strategy.
1003852
Upper Bounds of Entire Chromatic Number of Plane Graphs
The entire chromatic number χvef (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. Kronk and Mitchem (1973) conjectured that χvef (G) ≤ 1 + 4 for every plane graph G. In this paper we prove the conjecture for a plane graph G having χ ′(G) = 1 and give a upper bound χvef (G) ≤ 1+ 5 for all plane graphs, where χ ′(G) and 1 are the chromatic index and the maximum degree of G, respectively.
11186519
Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers
Let G be a graph of nonnegative characteristic and let g(G) and @D(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (1) @D(H)= =11; (2) @D(H)= =7; (3) @D(H)= =5 or G does not contain 4-cycles and 5-cycles; (4) @D(H)= =11; (2) col"g(G)= =7; (3) col"g(G)= =5 or G contains no 4-cycles and 5-cycles; (4) col"g(G)=<10 if G does not contain 4-cycles.
9810371
The edge-face choosability of plane graphs
A plane graph G is said to be k-edge-face choosable if, for every list L of colors satisfying |L(x)|=k for every edge and face x, there exists a coloring which assigns to each edge and each face a color from its list so that any adjacent or incident elements receive different colors. We prove that every plane graph G with maximum degree Δ(G) is (Δ(G)+3)-edge-face choosable.
28890
Extension of Lower Probabilities and Coherence of Belief Measures
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.
17166482
Benchmarking the effectiveness of sequential pattern mining methods
Recently, there is an increasing interest in new intelligent mining methods to find more meaningful and compact results. In intelligent data mining research, accessing the quality and usefulness of the results from different mining methods is essential. However, there is no general benchmarking criteria to evaluate whether these new methods are indeed more effective compared to the traditional methods. Here we propose a novel benchmarking criteria that can systematically evaluate the effectiveness of any sequential pattern mining method under a variety of situations. The benchmark evaluates how well a mining method finds known common patterns in synthetic data. Such an evaluation provides a comprehensive understanding of the resulting patterns generated from any mining method empirically. In this paper, the criteria are applied to conduct a detailed comparison study of the support-based sequential pattern model with an approximate pattern model based on sequence alignment. The study suggests that the alignment model will give a good summary of the sequential data in the form of a set of common patterns in the data. In contrast, the support model generates massive amounts of frequent patterns with much redundancy. This suggests that the results of the support model require more post processing before it can be of actual use in real applications.
5616933
Techniques for effective vocabulary selection
The vocabulary of a continuous speech recognition (CSR) system is a significant factor in determining its performance. In this paper, we present three principled approaches to select the target vocabulary for a particular domain by trading off between the target out-of-vocabulary (OOV) rate and vocabulary size. We evaluate these approaches against an ad-hoc baseline strategy. Results are presented in the form of OOV rate graphs plotted against increasing vocabulary size for each technique.
8256320
Fast computation with neural oscillators
This paper studies new spike-based models for winner-take-all computation and coincidence detection. In both cases, fast convergence is achieved independent of initial conditions, and network complexity is linear in the number of inputs. Fully distributed versions can be modelled based on groups of interneurons connected through electrical synapses.
2992545
Constrained 3D shape reconstruction using a combination of surface fitting and registration
We investigate 3D shape reconstruction from measurement data in the presence of constraints. The constraints may fix the surface type or set geometric relations between parts of an object's surface, such as orthogonality, parallelity and others. It is proposed to use a combination of surface fitting and registration within the geometric optimization framework of squared distance minimization (SDM). In this way, we obtain a quasi-Newton like optimization algorithm, which in each iteration simultaneously registers the data set with a rigid motion to the fitting surface and adapts the shape of the fitting surface. We present examples to show the applicability of our method to constrained 3D shape fitting for reverse engineering of CAD models and to high accuracy fitting with kinematic surfaces, which include surfaces of revolution (reconstructed from fragments of archeological pottery) and spiral surfaces, which are fitted to 3D measurement data of shells. Our optimization algorithm can combine registration of multiple scans of an object and model fitting into a single optimization process which is shown to be superior to the traditional procedure, which first registers the data and then fits a model to it.