2932097
Circular Chromatic Number of Planar Graphs of Large Odd Girth
It was conjectured by Jaeger that $4k$-edge connected graphs admit a $(2k+1, k)$-flow. The restriction of this conjecture to planar graphs is equivalent to the statement that planar graphs of girth at least $4k$ have circular chromatic number at most $2+ {{1}\over {k}}$. Even this restricted version of Jaeger's conjecture is largely open. The $k=1$ case is the well-known Grotzsch 3-colour theorem. This paper proves that for $k \geq 2$, planar graphs of odd girth at least $8k-3$ have circular chromatic number at most $2+{{1}\over {k}}$.
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.
7791840
Pseudo-Hamiltonian-connected graphs
Abstract Given a graph G and a positive integer k , denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k . A graph G is called pseudo- k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo- k Hamiltonian-connected for some positive integer k . This paper proves that a graph G is pseudo-Hamiltonian-connected if and only if for every non-empty proper subset X of V(G) , |N(X)|>|X| . The proof of the characterization also provides a polynomial-time algorithm that decides whether or not a given graph is pseudo-Hamiltonian-connected. The characterization of pseudo-Hamiltonian-connected graphs also answers a question of Richard Nowakowski, which motivated this paper.
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).
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.
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.
147992
A hierarchical access control model for video database systems
Content-based video database access control is becoming very important, but it depends on the progresses of the following related research issues: (a) efficient video analysis for supporting semantic visual concept representation; (b) effective video database indexing structure; (c) the development of suitable video database models; and (d) the development of access control models tailored to the characteristics of video data. In this paper, we propose a novel approach to support multilevel access control in video databases. Our access control technique combines a video database indexing mechanism with a hierarchical organization of visual concepts (i.e., video database indexing units), so that different classes of users can access different video elements or even the same video element with different quality levels according to their permissions. These video elements, which, in our access control mechanism, are used for specifying the authorization objects, can be a semantic cluster, a subcluster, a video scene, a video shot, a video frame, or even a salient object (i.e., region of interest). In the paper, we first introduce our techniques for obtaining these multilevel video access units. We also propose a hierarchical video database indexing technique to support our multilevel video access control mechanism. Then, we present an innovative access control model which is able to support flexible multilevel access control to video elements. Moreover, the application of our multilevel video database modeling, representation, and indexing for MPEG-7 is discussed.
6927660
Scalable Representative Instance Selection and Ranking
Finding a small set of representative instances for large datasets can bring various benefits to data mining practitioners so they can (1) build a learner superior to the one constructed from the whole massive data; and (2) avoid working on the whole original dataset all the time. We propose in this paper a scalable representative instance selection and ranking (SRISTAR pronounced 3STAR) mechanism, which carries two unique features: (1) it provides a representative instance ranking list, so that users can always select instances from the top to the bottom, based on the number of examples they prefer; and (2) it investigates the behaviors of the underlying examples for instance selection, and the selection procedure tries to optimize the expected future error. Given a dataset, we first cluster instances into small data cells, each of which consists of instances with similar behaviors. Then we progressively evaluate data cells and their combinations, and order them into a list such that the learners built from the top cells are more accurate
5944615
Eliminating Class Noise in Large Datasets
This paper presents a new approach for identifying and eliminating mislabeled instances in large or distributed datasets. We first partition a dataset into subsets, each of which is small enough to be processed by an induction algorithm at one time. We construct good rules from each subset, and use the good rules to evaluate the whole dataset. For a given instance Ik, two error count variables are used to count the number of times it has been identified as noise by all subsets. The instance with higher error values will have a higher probability of being a mislabeled example. Two threshold schemes, majority and non-objection, are used to identify the noise. Experimental results and comparative studies from real-world datasets are reported to evaluate the effectiveness and efficiency of the proposed approach.
31920818
Automatic model-based semantic object extraction algorithm
Automatic image segmentation and object extraction play an important role in supporting content-based image coding, indexing, and retrieval. However, the low-level visual homogeneity critical (like color, texture, intensity, and so on) for segmentation do not lead to semantic objects directly because a semantic object can contain totally different gray levels, color, or texture. We propose an automatic model-based semantic object extraction algorithm by integrating object seeds with their region constraint graphs (perceptual models). Images are first partitioned into a set of homogeneous regions with accurate boundaries by integrating the results obtained by similarity-based region growing and edge detection procedures. We propose a 1-D fast entropic thresholding technique for determining the thresholds used in region growing and edge detection automatically. The object seeds, which are the intuitive and representative parts of semantic objects, are then distinguished from these homogeneous image regions. A seeded region aggregation procedure is used for merging the adjacent regions of a detected object seed to give a semantic object according to the perceptual model of the object. We focus on semantic human object generation by taking faces as object seeds and using a ratio-based perceptual model.
6174679
Correlation Clustering for Crosslingual Link Detection
The crosslingual link detection problem calls for identifying news articles in multiple languages that report on the same news event. This paper presents a novel approach based on constrained clustering. We discuss a general way for constrained clustering using a recent, graph-based clustering framework called correlation clustering. We introduce a correlation clustering implementation that features linear program chunking to allow processing larger datasets. We show how to apply the correlation clustering algorithm to the crosslingual link detection problem and present experimental results that show correlation clustering improves upon the hierarchical clustering approaches commonly used in link detection, and, hierarchical clustering approaches that take constraints into account.