12426657
Ramsey families which exclude a graph
For graphsA andB the relationA→(B)r1 means that for everyr-coloring of the vertices ofA there is a monochromatic copy ofB inA. Forb (G) is the family of graphs which do not embedG. A familyℱof graphs is Ramsey if for all graphsB∈ℱthere is a graphA∈ℱsuch thatA→(B)r1. The only graphsG for which it is not known whether Forb (G) is Ramsey are graphs which have a cutpoint adjacent to every other vertex except one. In this paper we prove for a large subclass of those graphsG, that Forb (G) does not have the Ramsey property.
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.
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).
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.
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.
2283419
Nonparametric Transforms of Graph Kernels for Semi-Supervised Learning
We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.
14278266
Harmonic mixtures: combining mixture models and graph-based methods for inductive and scalable semi-supervised learning
Graph-based methods for semi-supervised learning have recently been shown to be promising for combining labeled and unlabeled data in classification problems. However, inference for graph-based methods often does not scale well to very large data sets, since it requires inversion of a large matrix or solution of a large linear program. Moreover, such approaches are inherently transductive, giving predictions for only those points in the unlabeled set, and not for an arbitrary test point. In this paper a new approach is presented that preserves the strengths of graph-based semi-supervised learning while overcoming the limitations of scalability and non-inductive inference, through a combination of generative mixture models and discriminative regularization using the graph Laplacian. Experimental results show that this approach preserves the accuracy of purely graph-based transductive methods when the data has "manifold structure," and at the same time achieves inductive learning with significantly reduced computational cost.
31441115
Seeded Semantic Object Generation toward Content-Based Video Indexing
A novel semantic object generation algorithm is proposed by collaborative integration of a new feature-based image segmentation technique and a seeded region aggregation procedure. The homogeneous image regions with closed boundaries are obtained by integrating the results of color edge detection and seeded region growing procedures. The object seeds are then distinguished from these homogeneous image regions. The semantic objects are finally generated by a seeded region aggregation procedure. The extracted semantic objects can then be tracked along the time axis. The video objects can then be used as the basic units for content-based video indexing.
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.
7014119
Discovering Relational Patterns across Multiple Databases
Relational patterns across multiple databases can reveal special pattern relationships hidden inside data collections. Existing research in data mining has made significant efforts in discovering different types of patterns from single or multiple databases, but how to find patterns that have a higher support in database A than in database B with a given support threshold a is still an open problem. We propose in this paper DRAMA, a systematic framework for discovering relational patterns across multiple databases. More specifically, given a series of data collections, we try to discover patterns from different databases with patterns' relationships satisfying the user specified constraints. Our method seeks to build a hybrid frequent pattern tree (HFP-tree) from multiple databases, and mine patterns from the HFP-tree by integrating users' constraints into the pattern mining process.