5245849
On Independent Cycles in a Bipartite Graph
Abstract. Let G=(V1,V2;E) be a bipartite graph with 2k≤m=|V1|≤|V2|=n, where k is a positive integer. We show that if the number of edges of G is at least (2k−1)(n−1)+m, then G contains k vertex-disjoint cycles, unless e(G)=(2k−1)(n−1)+m and G belongs to a known class of graphs.
17469562
Existence of two disjoint long cycles in graphs
Let n,h be integers with n>=6 and h>=7. We prove that if G is a graph of order n with @s"2(G)>=h, then G contains two disjoint cycles C"1 and C"2 such that |V(C"1)|+|V(C"2)|>=min{h,n}.
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).
43159264
P2p-factorization of a complete bipartite graph
39356858
Vertex-disjoint quadrilaterals in graphs
Let k be a positive integer and G a graph of order n. In (Discrete Math. 203 (1999) 229), we proved that if n=4k and @d(G)>=2k then G contains k-1 vertex-disjoint quadrilaterals. In this paper, we investigate vertex-disjoint quadrilaterals in G with n@?0(mod4), and we have found the best minimum degree condition @d(G)>=@?12n@? such that G contains @?14n@? vertex-disjoint quadrilaterals. As a result of our method, we have improved our previous result as follows: If n=4k and @d(G)>=2k-1 then G contains k-1 vertex-disjoint quadrilaterals.
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).
2699916
Deception Detection Via Blob Motion Pattern Analysis
Deception dectection is one of the most difficult problems in affect recognition and expression research area. Recently, non-verbal methods of detecting deception have appeared to be promising. Thomas[1] presented a proof-of-concept study based on the blob analysis of some suspects' interviews and mock experiments video clips. In this paper, we present our recent research work in the direction of developing an automated deception detection system. We propose a blob motion pattern analysis approach to solve this problem.
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. >
36856889
Prime Cube Graph Approach for Processor Allocation in Hypercube Multiprocessors
28692587
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
37941718
Generalized discrete-time PI control of output PDFs using square root B-spline expansion
A new control approach is proposed for the probability density function (PDF) control of non-Gaussian stochastic systems using PI controllers. Using the square root output PDF model and the weight dynamics, the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics, where LMI techniques are used to design a generalized PI controller such that stability, state constraints and tracking performances can be guaranteed simultaneously.