20473974
4-Colorable 6-regular toroidal graphs
This paper proves two conjectures of Collins, Fisher and Hutchinson about the chromatic number of some circulant graphs. As a consequence, we characterize 4-colorable 6-regular toroidal 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.
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.
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.
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.
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.
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
9199797
Error Detection and Impact-Sensitive Instance Ranking in Noisy Datasets
Given a noisy dataset, how to locate erroneous instances and attributes and rank suspicious instances based on their impacts on the system performance is an interesting and important research issue. We provide in this paper an Error Detection and Impact-sensitive instance Ranking (EDIR) mechanism to address this problem. Given a noisy dataset D, we first train a benchmark classifier T from D. The instances, that cannot be effectively classified by T are treated as suspicious and forwarded to a subset S. For each attribute Ai, we switch Ai and the class label C to train a classifier APi for Ai. Given an instance Ik in S, we use APi and the benchmark classifier T to locate the erroneous value of each attribute Ai. To quantitatively rank instances in S, we define an impact measure based on the Information-gain Ratio (IR). We calculate IRi between attribute Ai and C, and use IRi as the impact-sensitive weight of Ai. The sum of impact-sensitive weights from all located erroneous attributes of Ik indicates its total impact value. The experimental results demonstrate the effectiveness of our strategies.
15136742
Mining Complex Patterns across Sequences with Gap Requirements
The recurring appearance of sequential patterns, when confined by the predefined gap requirements, often implies strong temporal correlations or trends among pattern elements. In this paper, we study the problem of mining a set of gap constrained sequential patterns across multiple sequences. Given a set of sequences S1, S2,., SK constituting a single hypersequence S, we aim to find recurring patterns in S, say P, which may cross multiple sequences with all their matching characters in S bounded by the user specified gap constraints. Because of the combinatorial candidate explosion, traditional Apriori-based algorithms are computationally infeasible. Our research proposes a new mechanism to ensure pattern growing and pruning. When combining the pruning technique with our Gap Constrained Search (GCS) and map-based support prediction approaches, our method achieves a speed about 40 times faster than its other peers.
1166908
Distributed rate allocation for multi-stream video transmission over ad hoc networks
When multiple video streams are present in an ad hoc network, they share and compete for the common network resources. A rate allocation algorithm must balance the available resources among the video streams in a fair and efficient manner. In addition, it is desirable to have a distributed solution so that nodes do not need to collect global information of the network and that the computational burden can be shared. We propose a distributed rate allocation algorithm which minimizes the total distortion of all video streams. Based on the subgradient method, the proposed scheme only requires link price updates at each relay node based on local observations and rate adaptations at each source node derived from rate-distortion (RD) models of the video. Simulation results show that the proposed scheme can achieve the same optimal rate allocation as that obtained from exhaustive search.