17658871
On generalized Ramsey numbers
Abstract Let f 1 and f 2 be graph parameters. The Ramsey number r ( f 1 ⩾ m ; f 2 ⩾ n ) is defined as the minimum integer N such that any graph G on N vertices, either f 1 ( G )⩾ m or f 2 ( G )⩾n . A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t ( G ). We verify that (1−o(1))(24 n ) 1/3 ⩽ r ( t ⩾ n ; t ⩾ n )⩽(1+o(1))(48 n ) 1/3 as n →∞.
2037433
An upper bound for ramsey numbers
Let G″ be a graph obtained from G by deleting two vertices. It is shown that r(G, H) ⩽ A + B + 2 + 2 (A2 + AB + B2)3 where A = r(G″, H) and B = r(G,H″).
34644814
The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a Ck-free graph is at least c1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(Ck, Kn) is at most c2(nm + 1/log n)1/m, where c1 = c1(m) > 0 and c2 = c2(m) > 0.
206570728
On Book-Complete Graph Ramsey Numbers
It is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1, mas a subgraph has independence number at leastNf(d), wheref(x)~(logx/x)(x?∞). From this result we find that the book-complete graph Ramsey number satisfiesr(Bm, Kn)?mn2/log(n/e). It is also shown that for every treeTmwithmedges,r(K1+Tm,Kn)?(2m?1)n2/log(n/e).
34447441
Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers
Abstract The Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K 2,m ,K n )⩽(m−1+ o (1))(n/ log n) 2 and r(C 2m ,K n )⩽c(n/ log n) m/(m−1) for m fixed and n→∞. Also r(K 2,n ,K n )=Θ(n 3 / log 2 n) and r(C 5 ,K n )⩽cn 3/2 / log n .
43234278
A Ramsey Goodness Result for Graphs with Many Pendant Edges
24872800
Face Recognition using Patch-based Spin Images
This paper explores how spin images can be constructed using shape-from-shading information and used for the purposes of face recognition. We commence by extracting needle-maps from gray-scale images of faces, using a mean needle-map to enforce the correct pattern official convexity and concavity. Spin images (Johnson and Hebert, 1999) are estimated from the needle maps using local spherical geometry to approximate the facial surface. Our representation is based on the spin image histograms for an arrangement of image patches. We demonstrate how this representation can be used to perform face recognition across different subjects and illumination conditions. Experiments show the method to be reliable and accurate
6625111
On incremental and robust subspace learning
Principal Component Analysis (PCA) has been of great interest in computer vision and pattern recognition. In particular, incrementally learning a PCA model, which is computationally efficient for large-scale problems as well as adaptable to reflect the variable state of a dynamic system, is an attractive research topic with numerous applications such as adaptive background modelling and active object recognition. In addition, the conventional PCA, in the sense of least mean squared error minimisation, is susceptible to outlying measurements. To address these two important issues, we present a novel algorithm of incremental PCA, and then extend it to robust PCA. Compared with the previous studies on robust PCA, our algorithm is computationally more efficient. We demonstrate the performance of these algorithms with experimental results on dynamic background modelling and multi-view face modelling.
35929
Robust Head Tracking with Particles Based on Multiple Cues Fusion
This paper presents a fully automatic and highly robust head tracking algorithm based on the latest advances in real-time multi-view face detection techniques and multiple cues fusion under particle filter framework. Visual cues designed for general object tracking problem hardly suffice for robust head tracking under diverse or even severe circumstances, making it a necessity to utilize higher level information which is object-specific. To this end we introduce a vector-boosted multi-view face detector [2] as the “face cue” in addition to two other general visual cues targeting the entire head, color spatiogram[3] and contour gradient. Data fusion is done by an extended particle filter which supports multiple distinct yet interrelated state vectors (referring to face and head in our tracking context). Furthermore, pose information provided by the face cue is exploited to help achieve improved accuracy and efficiency in the fusion. Experiments show that our algorithm is highly robust against target position, size and pose change as well as unfavorable conditions such as occlusion, poor illumination and cluttered background.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
6040880
Rupture degree of graphs
We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph K n is defined as 1−n, and the rupture degree for an incomplete connected graph G is defined by r(G)=max{ω(G−X)−|X|−m(G−X):X⊂V(G), ω(G−X)>1}, where ω(G−X) is the number of components of G−X and m(G−X) is the order of a largest component of G−X. It is shown that this parameter can be used to measure the vulnerability of networks. Rupture degrees of several specific classes of graphs are determined. Formulas for the rupture degree of join graphs and some bounds of the rupture degree are given. We also obtain some Nordhaus–Gaddum type results for the rupture degree.