28979330
Connected Factors and Spanning Trees in Graphs
Abstract. Let G be a graph, and g, f, f′ be positive integer-valued functions defined on V(G). If an f′-factor of G is a spanning tree, we say that it is f′-tree. In this paper, it is shown that G contains a connected (g, f+f′−1)-factor if G has a (g, f)-factor and an f′-tree.
5196479
Odd Wheels in Graphs
For k?1 the odd wheel of 2k+1 spokes, denoted by W2k+1, is the graph obtained from a cycle of length 2k+1 by adding a new vertex and joining it to all vertices of the cycle. In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes.
8227025
A Browser Compatibility Testing Method Based on Combinatorial Testing
For ensuring the displaying effects of Web applications, it is important to perform compatibility testing for browsers under the different configurations and it is a hard task to test all. So this paper focused on the improvements for browser compatibility testing. Firstly, we introduced the related work. Then we analysed the functional speciality of the current popular browsers, and provided the preconditions to simplify problems. Next we gave an instance and brought forward the single factor covering method and the pair-wise covering design to gain testing suits. Finally, we introduced the assistant tools we have developed and the future work.
33924916
Geometric Algorithms for Density-Based Data Clustering
We present new geometric approximation and exact algorithms for the density-based data clustering problem in d-dimensional space Rd (for any constant integer d ? 2). Previously known algorithms for this problem are efficient only for uniformly-distributed points. However, these algorithms all run in ?(n2) time in the worst case, where n is the number of input points. Our approximation algorithm based on the ?-fuzzy distance function takes O(n log n) time for any given fixed value ? > 0, and our exact algorithms take sub-quadratic time. The running times and output quality of our algorithms do not depend on any particular data distribution. We believe that our fast approximation algorithm is of considerable practical importance, while our sub-quadratic exact algorithms are more of theoretical interest. We implemented our approximation algorithm and the experimental results show that our approximation algorithm is efficient on arbitrary input point sets.
38400231
On mixed Ramsey numbers
Abstract For a graph theoretic parameter f , an integer m and a graph H , the mixed Ramsey number v(f; m; H) is defined as the least positive integer p such that if G is any graph of order p , then either f(G) ⩾ m or Ḡ contains a subgraph isomorphic to H . Let ϱ denote vertex linear arboricity and let H be any connected graph of order n . In this note we show that v(ϱ; m; H) = 1 + (n + n p ( H ) − 2)(m − 1) , where n p ( H ) is the path partition number of H .
39744832
On signed edge domination numbers of graphs
Abstract Given a graph G=(V,E) , if e=uv∈E , then the closed edge-neighbourhood of e is denoted by N[e]={u′v′∈E|u′=u or v′=v} . A function f : E→{+1,−1} is called the signed edge domination function (SEDF) of G if ∑ e′∈N[e] f(e′)⩾1 for every e∈E . The signed edge domination number γ s ′(G) of G is defined as γ s ′(G)= min {∑ e∈E f(e) | f is an SEDF of G} . Let Ψ(m)= min {γ s ′(H)|H is a graph with |E(H)|=m} . In this paper, we determine the exact value of Ψ(m) for each positive integer m . That is: Ψ(m)=2 1 3 24m+25 +6m+5 6 −m, where ⌈x⌉ denotes the ceiling of x . In addition, we also characterize all connected graphs G with γ s ′(G)=|E(G)| .
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).