36146387
On Hedetniemi's conjecture and the colour template scheme
Hedetniemi's conjecture states that the chromatic number of a product of graphs is the minimum of the chromatic numbers of the factors. El-Zahar and Sauer (Combinatorica 5 (1985) 121) have shown that the chromatic number of a product of 4-chromatic graphs is 4. In this paper, we investigate to which extent their methods can be adapted to the case of 5-chromatic graphs. Our main result is that if G and H are connected graphs of chromatic number at least 5 that both contain odd wheels as subgraphs, then their product also has chromatic number at least 5. However, we also provide counterexamples to the El-Zahar and Sauer conjecture on the structure of n-chromatic subgraphs of products of n-chromatic graphs. This implies that the method of El-Zahar and Sauer will not be sufficient to prove all cases of Hedetniemi's conjecture for chromatic numbers larger than 4.
10777147
Circular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs
This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphsG(Z,D) for various distance setsD. In particular, we determine these numbers for thoseDsets of size two, for some specialDsets of size three, forD= {1, 2,···,m,n} with 1 ?m < n, forD= {q,q+1,···,p} withq
206792834
Star chromatic numbers of graphs
We investigate the relation between the star-chromatic number χ(G) and the chromatic number χ(G) of a graphG. First we give a sufficient condition for graphs under which their starchromatic numbers are equal to their ordinary chromatic numbers. As a corollary we show that for any two positive integersk, g, there exists ak-chromatic graph of girth at leastg whose star-chromatic number is alsok. The special case of this corollary withg=4 answers a question of Abbott and Zhou. We also present an infinite family of triangle-free planar graphs whose star-chromatic number equals their chromatic number. We then study the star-chromatic number of An infinite family of graphs is constructed to show that for each ε>0 and eachm≥2 there is anm-connected (m+1)-critical graph with star chromatic number at mostm+ε. This answers another question asked by Abbott and Zhou.
5956515
Homomorphisms to oriented paths
Abstract Given an oriented path P , we characterize those digraphs G which are homomorphic to P . The characterization equates the nonexistence of a homomorphism G → P with the existence of a homomorphism W → G , for some oriented path W which is not homomorphic to P . This result complements the recent polynomial time algorithm of Welzl et al. to find such a homomorphism (if one exists).
17776907
Circular perfect graphs
For 1 ≤ d ≤ k, let Kk/d be the graph with vertices 0, 1, · · · , k − 1, in which i ∼ j if d ≤ |i − j| ≤ k − d. The circular chromatic number χc(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to Kk/d. The circular clique number ωc(G) of G is the maximum of those k/d for which Kk/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G we have χc(H) = ωc(H). This paper surveys results on circular perfect graphs.
42953989
The game coloring number of pseudo partial k-trees
Abstract This paper introduces a new class of graphs: (a,b)-pseudo partial k-trees. In some sense, the parameters (a,b) measure a graph's deviation from being a partial k-tree. In particular, a (0,0)-pseudo partial k-tree is just a partial k-tree. We discuss the game coloring number (as well as the game chromatic number) of (a,b)-pseudo partial k-trees, and prove that the game coloring number of an (a,b)-pseudo partial k-tree is at most 3k+2a+b+2. In particular, the game coloring number of a partial k-tree is at most 3k+2. This reduces considerably the previous known upper bound for the game chromatic number of a partial k-tree. Then we describe another strategy for Alice for playing the game, which gives a better upper bound for the game coloring number of (a,b)-pseudo partial 2-trees. Namely, we prove that the game coloring number of an (a,b)-pseudo partial 2-tree is at most a+b+8. By using this result, we prove that the game coloring number of a graph embeddable on an orientable surface of genus g⩾1 is at most ⌊ 1 2 (3 1+48g +23)⌋. This is the first upper bound for the game coloring number of such graphs, and it also improves considerably the previous known upper bound for the game chromatic number of such graphs. Moreover, the strategy for Alice introduced in this paper for playing the game can be considered as a common generalization of the previous known strategies for playing the game on forests, interval graphs, outerplanar graphs and planar graphs.
1786671
Light field compression using disparity-compensated lifting and shape adaptation
We propose disparity-compensated lifting for wavelet compression of light fields. With this approach, we obtain the benefits of wavelet coding, such as scalability in all dimensions, as well as superior compression performance. Additionally, the proposed approach solves the irreversibility limitations of previous light field wavelet coding approaches, using the lifting structure. Our scheme incorporates disparity compensation into the lifting structure for the transform across the views in the light field data set. Another transform is performed to exploit the coherence among neighboring pixels, followed by a modified SPIHT coder and rate-distortion optimized bitstream assembly. A view-sequencing algorithm is developed to organize the views for encoding. For light fields of an object, we propose to use shape adaptation to improve the compression efficiency and visual quality of the images. The necessary shape information is efficiently coded based on prediction from the existing geometry model. Experimental results show that the proposed scheme exhibits superior compression performance over existing light field compression techniques.
6597740
Semi-supervised classification with hybrid generative/discriminative methods
We compare two recently proposed frameworks for combining generative and discriminative probabilistic classifiers and apply them to semi-supervised classification. In both cases we explore the tradeoff between maximizing a discriminative likelihood of labeled data and a generative likelihood of labeled and unlabeled data. While prominent semi-supervised learning methods assume low density regions between classes or are subject to generative modeling assumptions, we conjecture that hybrid generative/discriminative methods allow semi-supervised learning in the presence of strongly overlapping classes and reduce the risk of modeling structure in the unlabeled data that is irrelevant for the specific classification task of interest. We apply both hybrid approaches within naively structured Markov random field models and provide a thorough empirical comparison with two well-known semi-supervised learning methods on six text classification tasks. A semi-supervised hybrid generative/discriminative method provides the best accuracy in 75% of the experiments, and the multi-conditional learning hybrid approach achieves the highest overall mean accuracy across all tasks.
1057136
Corrective Classification: Classifier Ensembling with Corrective and Diverse Base Learners
Empirical studies on supervised learning have shown that ensembling methods lead to a model superior to the one built from a single learner under many circumstances especially when learning from imperfect, such as biased or noise infected, information sources. In this paper, we provide a novel corrective classification (C2) design, which incorporates error detection, data cleansing and Bootstrap sampling to construct base learners that constitute the classifier ensemble. The essential goal is to reduce noise impacts and eventually enhance the learners built from noise corrupted data. We further analyze the importance of both the accuracy and diversity of base learners in ensembling, in order to shed some light on the mechanism under which C2 works. Experimental comparisons will demonstrate that C2 is not only superior to the learner built from the original noisy sources, but also more reliable than bagging or the aggressive classifier ensemble (ACE), which are two degenerate components/variants of C2.
3813357
Video data mining: semantic indexing and event detection from the association perspective
Advances in the media and entertainment industries, including streaming audio and digital TV, present new challenges for managing and accessing large audio-visual collections. Current content management systems support retrieval using low-level features, such as motion, color, and texture. However, low-level features often have little meaning for naive users, who much prefer to identify content using high-level semantics or concepts. This creates a gap between systems and their users that must be bridged for these systems to be used effectively. To this end, in this paper, we first present a knowledge-based video indexing and content management framework for domain specific videos (using basketball video as an example). We will provide a solution to explore video knowledge by mining associations from video data. The explicit definitions and evaluation measures (e.g., temporal support and confidence) for video associations are proposed by integrating the distinct feature of video data. Our approach uses video processing techniques to find visual and audio cues (e.g., court field, camera motion activities, and applause), introduces multilevel sequential association mining to explore associations among the audio and visual cues, classifies the associations by assigning each of them with a class label, and uses their appearances in the video to construct video indices. Our experimental results demonstrate the performance of the proposed approach.
45349056
Automatic Scene Detection in News Program by Integrating Visual Feature and Rules
Organizing video sequences from shot level to scene level is a challenging task, however, without the scene information, it will be very hard to extract the content of the video. In this paper, a visual and rule information integrated strategy is proposed to detect the scene information of the News programs. First, we extract out the video caption and anchor person (AP) shots in the video. Second, the rules among the scene, video caption, AP shots will be used to detect the scenes. Third, the visual features will also be used to analysis the scene information in the region which can not be covered by the rules. And experimental results based on this strategy are provided and analyzed on broadcast News videos.