14354011
A study of the total chromatic number of equibipartite graphs
Abstract The total chromatic number χ t ( G ) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibipartite graphs of order 2 n with maximum degree n − 1. As a part of our results, we disprove the biconformability conjecture.
12831347
Equitable Coloring and the Maximum Degree
Abstract Let Δ(G) denote the maximum degree of a graph G . The equitable Δ-coloring conjecture asserts that a connected graph G is equitably Δ( G )-colorable if it is different from K m , C 2 m + 1 and K 2 m + 1,2 m + 1 for all m ⩾ 1. This conjecture is established for graphs G satisfying Δ( G ) ⩾ | G |/2 or Δ( G ) ⩽ 3.
42366271
A Note on the m-Bounded Chromatic Number of a Tree
Abstract The m-bounded chromatic number of a graph G is the smallest number of colors required for a proper coloring of G in which each color is used at most m times. We will establish an exact formula for the m -bounded chromatic number of a tree.
16166391
Linear k-arboricities on trees
Abstract For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number l such that the edge set E(G) can be partitioned into l disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)⩽m.
38200007
Total colorings of equibipartite graphs
Abstract The total chromatic number χτ ( G ) of a graph G is the least number of colors needed to color the vertices and the edges of G such that no adjacent or incident pair of elements receive the same color. A simple graph G is called type 1 if χτ ( G ) = Δ ( G ) + 1, where Δ ( G ) is the maximum degree of G . In this paper we prove the following conjecture of Chen et al.: An ( n − 2)-regular equibipartite graph K n , n − E ( J ) is type 1 if and only if J contains a 4-cycle.
16547141
Edge domination in complete partite graphs
Abstract An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D . An edge domatic partition of a graph G =( V , E ) is a collection of pairwise-disjoint edge dominating sets of G whose union is E . The maximum size of an edge domatic partition of G is called the edge domatic number . In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split graphs .
6763688
Paint Inspired Color Mixing and Compositing for Visualization
Color is often used to convey information, and color compositing is often required while visualizing multiattribute information. This paper proposes an alternative method for color compositing. In order to present understandable color blending to the general public, several techniques are proposed. First, a paint-inspired RYB color space is used. In addition, noise patterns are employed to produce subregions of pure color within an overlapped region. We show examples to demonstrate the effectiveness of our technique for visualization
13073706
Graph homotopy and Graham homotopy
Abstract Simple-homotopy for cell complexes is a special type of topological homotopy constructed by elementary collapses and elementary expansions. In this paper, we introduce graph homotopy for graphs and Graham homotopy for hypergraphs and study the relation between the two homotopies and the simple-homotopy for cell complexes. The graph homotopy is useful to describe topological properties of discretized geometric figures, while the Graham homotopy is essential to characterize acyclic hypergraphs and acyclic relational database schemes.
1586078
Dual photography
We present a novel photographic technique called dual photography, which exploits Helmholtz reciprocity to interchange the lights and cameras in a scene. With a video projector providing structured illumination, reciprocity permits us to generate pictures from the viewpoint of the projector, even though no camera was present at that location. The technique is completely image-based, requiring no knowledge of scene geometry or surface properties, and by its nature automatically includes all transport paths, including shadows, inter-reflections and caustics. In its simplest form, the technique can be used to take photographs without a camera; we demonstrate this by capturing a photograph using a projector and a photo-resistor. If the photo-resistor is replaced by a camera, we can produce a 4D dataset that allows for relighting with 2D incident illumination. Using an array of cameras we can produce a 6D slice of the 8D reflectance field that allows for relighting with arbitrary light fields. Since an array of cameras can operate in parallel without interference, whereas an array of light sources cannot, dual photography is fundamentally a more efficient way to capture such a 6D dataset than a system based on multiple projectors and one camera. As an example, we show how dual photography can be used to capture and relight scenes.
10957724
Footprint area sampled texturing
We study texture projection based on a four region subdivision: magnification, minification, and two mixed regions. We propose improved versions of existing techniques by providing exact filtering methods which reduce both aliasing and overblurring, especially in the mixed regions. We further present a novel texture mapping algorithm called FAST (footprint area sampled texturing), which not only delivers high quality, but also is efficient. By utilizing coherence between neighboring pixels, performing prefiltering, and applying an area sampling scheme, we guarantee a minimum number of samples sufficient for effective antialiasing. Unlike existing methods (e.g., MlP-map, Feline), our method adapts the sampling rate in each chosen MlP-map level separately to avoid undersampling in the lower level l for effective antialiasing and to avoid oversampling in the higher level l+1 for efficiency. Our method has been shown to deliver superior image quality to Feline and other methods while retaining the same efficiency. We also provide implementation trade offs to apply a variable degree of accuracy versus speed.
2373278
A discriminative HMM/N-gram-based retrieval approach for mandarin spoken documents
In recent years, statistical modeling approaches have steadily gained in popularity in the field of information retrieval. This article presents an HMM/N-gram-based retrieval approach for Mandarin spoken documents. The underlying characteristics and the various structures of this approach were extensively investigated and analyzed. The retrieval capabilities were verified by tests with word- and syllable-level indexing features and comparisons to the conventional vector-space model approach. To further improve the discrimination capabilities of the HMMs, both the expectation-maximization (EM) and minimum classification error (MCE) training algorithms were introduced in training. Fusion of information via indexing word- and syllable-level features was also investigated. The spoken document retrieval experiments were performed on the Topic Detection and Tracking Corpora (TDT-2 and TDT-3). Very encouraging retrieval performance was obtained.