2785443
An upper bound on the number of edges of edge-coloring critical graphs with high maximum degree
In this paper, we prove that any edge-coloring critical graph G with maximum degree @D>=([email protected])/2, where @e= =8 and |V(G)|>[email protected]@d-4-(@D+6)/(@d-6), where @d is the minimum degree of G. It generalizes a result of Sanders and Zhao.
1502406
Total Coloring of Series-Parallel Graphs
32836256
Minimum average distance of strong orientations of graphs
The average distance of a graph (strong digraph) G, denoted by µ(G) is the average, among the distances between all pairs (ordered pairs) of vertices of G. If G is a 2-edge-connected graph, then µ→min(G) is the minimum average distance taken over all strong orientations of G. A lower bound for µ→min(G) in terms of the order, size, girth and average distance of G is established and shown to be sharp for several complete multipartite graphs. It is shown that there is no upper bound for µ→min(G) in terms of µ(G). However, if every edge of G lies on 3-cycle, then it is shown that µ→min(G) ≤ 7/4 µ(G). This bound is improved for maximal planar graphs to 5/3 µ(G) and even further to 3/2 µ(G) for eulerian maximal planar graphs and for outerplanar graphs with the property that every edge lies on 3-cycle. In the last case the bound is shown to be sharp.
45978330
Two sufficient conditions for a graph to be type 1
36178651
The vertex linear arboricity of distance graphs
A distance graph is a graph G(R,D) with the set of all points of the real line as vertex set and two vertices u,[email protected]?R are adjacent if and only if |u-v|@?D where the distance set D is a subset of the positive real numbers. Here, the vertex linear arboricity of G(R,D) is determined when D is an interval between 1 and @d. In particular, the vertex linear arboricity of integer distance graphs G(D) is discussed, too.
15322039
Tree coloring of distance graphs with a real interval set
Let RR be the set of real numbers and DD be a subset of the positive real numbers. The distance graph  G(R,D)G(R,D) is a graph with the vertex set RR and two vertices xx and yy are adjacent if and only if |x−y|∈D|x−y|∈D. In this work, the vertex arboricity (i.e., the minimum number of subsets into which the vertex set V(G)V(G) can be partitioned so that each subset induces an acyclic subgraph) of G(R,D)G(R,D) is determined for DD being an interval between 1 and δδ.
2718321
Face recognition with one training image per person
At present there are many methods that could deal well with frontal view face recognition. However, most of them cannot work well when there is only one training image per person. In this paper, an extension of the eigenface technique, i.e. projection-combined principal component analysis, (PC)2A, is proposed. (PC)2A combines the original face image with its horizontal and vertical projections and then performs principal component analysis on the enriched version of the image. It requires less computational cost than the standard eigenface technique and experimental results show that on a gray-level frontal view face database where each person has only one training image, (PC)2A achieves 3-5% higher accuracy than the standard eigenface technique through using 10-15% fewer eigenfaces.
30479706
Snooping fault-tolerant distributed shared memories
Abstract Distributed-memory systems that have no physically shared memory can be programmed by use of a shared-memory model by simulating a virtual shared address space. These distributed shared memory (DSM) systems can be easier to program than systems that use a message-passing model. However, as the number of processors implementing the DSM grows, the probability of failure grows. This article presents a set of fault-tolerant DSM (FTDSM) algorithms. The algorithms are derived from a system consisting of a set of processors connected by a broadcast network with one special processor, the snooper, that monitors network traffic. The snooper keeps a backup of the current state of the shared memory and can respond for failed processors. The addition of the snooper improves the reliability of the DSM at a lower cost than making each of the other processors fault tolerant. It is also shown how different degrees of application level fault tolerance can be incorporated into the FTDSM protocol to allow the recovery of application processes. The snooping FTDSM is extended to include multiple snoopers; then an integrated snooper FTDSM is developed that is not restricted to a broadcast network.
7218515
The Balanced Hypercube: A Cube-Based System for Fault-Tolerant Applications
In this paper, we present an interconnection structure, called the balanced hypercube, which is a variation of the standard hypercube with desirable properties of strong connectivity, regularity, and symmetry. The proposed structure is a special type of load balanced graph designed to tolerate processor failure. In balanced hypercubes, each processor has a backup (matching) processor that shares the same set of neighboring nodes. Therefore, tasks that run on a faulty processor can be reactivated in the backup processor to provide efficient system reconfiguration. Other properties of balanced hypercubes are examined. It is also shown that odd-dimensional balanced hypercubes have smaller diameters than that of standard hypercubes. As an application of balanced hypercubes, we show a fault-tolerant embedding of rings in balanced hypercubes.
23354749
Tight Bounds on the Number of l-Nodes in a Faulty Hypercube
The spanning binomial tree is one of most frequently used spanning tree structures to implement various parallel applications in multiprocessor systems, such as hypercubes. In this paper, we define...
204989501
On clique partitions of split graphs
Abstract Split graphs are graphs formed by taking a complete graph and an empty graph disjoint from it and some or all of the possible edges joining the two. We prove that the problem of deciding the clique partition number is NP-complete, even when restricted to the class of split graphs.