30781118
Vertex-disjoint hexagons with chords in a bipartite graph
Abstract In this paper, we explore vertex-disjoint subgraphs in a bipartite graph. Let G = ( V 1 , V 2 ; E ) be a bipartite graph with | V 1 | = | V 2 | = s k, where s ⩾ 2 and k ⩾ 1 are integers. We conjecture that if the minimum degree of G is at least ( s − 1) k + 1, then G contains k vertex-disjoint subgraphs isomorphic to K s,s . We verify this conjecture for k ⩽ 3. When s = 3, we show that G contains k vertex-disjoint hexagons such that each of them has two chords, i.e., G k( K 3,3 − e).
12358667
On Covering a Bipartite Graph with Cycles
We conjectured in [H. Wang, Australas. J. Combin., 19 (1999), pp. 115--121] that, for each integer $k\geq 2$, there exists N(k) such that if G=(V1,V2;E) is a bipartite graph with $|V_1|=|V_2|=n\geq N(k)$ and d(x)+d(y)\geq n+k$ for each pair of nonadjacent vertices x and y of G with $x\in V_1$ and $y\in V_2$, then for any k independent edges e1, . . ., ek of G, there exist k vertex-disjoint cycles C1, . . . ,Ck in G such that $e_i\in E(C_i)$ for all $i\in\{1,\ldots ,k\}$ and $V(C_1\cup\cdots \cup C_k)=V(G)$. This conjecture is also verified for k=2 in [H. Wang, Australas. J. Combin., 19 (1999), pp. 115--121]. We prove this conjecture for k=3 in this paper.
9527664
Vertex-Disjoint Triangles in Claw-Free Graphs with Minimum Degree at Least Three
. Our main result is as follows: For any integer , if G is a claw-free graph of order at least and with minimum degree at least 3, then G contains k vertex-disjoint triangles unless G is of order and G belongs to a known class of graphs. We also construct a claw-free graph with minimum degree 3 on n vertices for each such that it does not contain k vertex-disjoint triangles. We put forward a conjecture on vertex-disjoint triangles in -free graphs.
36127171
Packing Three Copies of a Tree into a Complete Graph
Abstract A three T of order n is said to be 3-placeable if there are three edge-disjoint copies of T in Kn. In this paper we characterize all the trees T such that T is 3-placeable.
34464594
On Quadrilaterals and Cycle Covers in a Bipartite Graph
30994252
An extension of a theorem on cycles containing specified independent edges
We give an alternative proof of a conjecture due to Wang (J. Graph Theory 26 (1997) 105) in a stronger form. The main theorem states that for any integer k ≥ 2 if G is a graph of order n ≥ 4k - 1 and d(u) + d(υ) ≥ n + 2k - 2 for each pair of non-adjacent vertices u and υ of G, then, for any k independent edges e1,... ,ek of G, there exist k vertex-disjoint cycles C1,..., Ck in G such that (i) ei ∈ E(Ci) for all 1 ≤ i ≤ k, (ii) V(C1)∪ ... ∪V(Ck) = V(G), and (iii) #{i ≤ k||Ci| a > n - 4k + 2). It strengthens the conjecture of Wang, which was first proven by Egawa et al. (Graphs Combin. 16 (2000) 81).
9557765
An ILC-Based Adaptive Control for General Stochastic Systems With Strictly Decreasing Entropy
In this paper, a new method for adaptive control of general nonlinear and non-Gaussian unknown stochastic systems has been proposed. The method applies the minimum entropy control scheme to decrease the closed-loop randomness of the output under an iterative learning control (ILC) basis. Both modeling and control of the plant are performed using dynamic neural networks. For this purpose, the whole control horizon is divided into a certain number of time domain subintervals called batches and a pseudo-D-type ILC law is employed to train the plant model and controller parameters so that the entropy of the closed-loop tracking error is made to decrease batch by batch. The method has the advantage of decreasing the output uncertainty versus the advances of batches along the time horizon. The analysis on the proposed ILC convergence is made and a set of demonstrable experiment results is also provided to show the effectiveness of the obtained control algorithm, where encouraging results have been obtained.
6565522
How to fool an unbounded adversary with a short key
The symmetric encryption problem which manifests itself when two parties must securely transmit a message m with a short shared secret key is considered in conjunction with a computationally unbounded adversary. As the adversary is unbounded, any encryption scheme must leak information about m; in particular, the mutual information between m and its ciphertext cannot be zero. Despite this, a family of encryption schemes is presented that guarantee that for any message space in {0,1}n with minimum entropy n-lscr and for any Boolean function h:{0,1}n rarr {0,1}, no adversary can predict h(m) from the ciphertext of m with more than 1/nomega(1)  advantage; this is achieved with keys of length lscr+omega(logn). In general, keys of length lscr+s yield a bound of 2-Theta(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently. Applications of this to cryptosystems based on complexity-theoretic assumptions are discussed and, in addition, a simplified proof of a fundamental "elision lemma" of Goldwasser and Micali is provided
29063745
A New Graph Approach to Minimizing Processor Fragmentation in Hypercube Multiprocessors
The authors propose a new approach for subcube and noncubic processor allocations for hypercube multiprocessors. The main idea is to represent available processors in the system by means of a prime cube graph (PC-graph). The PC-graph maintains the inter-relationships between free subcubes and hence reduces both internal and external processor fragmentations. Their simulation results show that the PC-graph approach outperforms the existing allocation strategies by 25% to 50% under certain load conditions. >
205762515
Minimum entropy of B-spline PDF systems with mean constraint
For the B-spline approximation of the continuous probability density function (PDF), the relationships between the B-spline weights and entropy both in general and under the mean constraint have been analyzed. It provides the conditions under which the minimum entropy can be achieved subject to the mean constraint. The difference between the entropy of continuous and discrete distributions has also been clarified. A minimum entropy controller with the mean constraint is then developed and several simulations are performed to verify the main results. (c) 2006 Elsevier Ltd. All rights reserved.
206733269
A Fast and Robust Ellipse Detection Algorithm Based on Pseudo-random Sample Consensus
Ellipse is one of the most common features that appears in images. Over years in research, real-timing and robustness have been two very challenging problems aspects of ellipse detection. Aiming to tackle them both, we propose an ellipse detection algorithm based on pseudo-random sample consensus (PRANSAC). In PRANSAC we improve a contour-based ellipse detection algorithm (CBED), which was presented in our previous work. In addition, the parallel thinning algorithm is employed to eliminate useless feature points, which increases the time efficiency of our detection algorithm. In order to further speed up, a 3-point ellipse fitting method is introduced. In terms of robustness, a "robust candidate sequence" is proposed to improve the robustness performance of our detection algorithm. Compared with the state-of-the-art ellipse detection algorithms, experimental results based on real application images show that significant improvements in time efficiency and performance robustness of the proposed algorithm have been achieved.