1502406
Total Coloring of Series-Parallel Graphs
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.
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
17157380
Optimal broadcasting in injured hypercubes using directed safety levels
A coating composition for polyolefinic films, especially poly-propylene films, which consists essentially of a solution of a dry three-component polymeric system comprising: (a) a first component consisting of acrylic homopolymers, copolymers or mixtures thereof; (b) a second component consisting of a polyester resin obtained by condensation; and (c) a third component consisting of medium or low viscosity nitrocellulose or mixtures thereof. The coated products and the coating process are also covered.
15943479
Efficient face candidates selector for face detection
Abstract In this paper an efficient face candidates selector is proposed for face detection tasks in still gray level images. The proposed method acts as a selective attentional mechanism. Eye-analogue segments at a given scale are discovered by finding regions which are roughly as large as real eyes and are darker than their neighborhoods. Then a pair of eye-analogue segments are hypothesized to be eyes in a face and combined into a face candidate if their placement is consistent with the anthropological characteristic of human eyes. The proposed method is robust in that it can deal with illumination changes and moderate rotations. A subset of the FERET data set and the BioID face database are used to evaluate the proposed method. The proposed face candidates selector is successful in 98.75% and 98.6% cases, respectively.
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.
811613
Efficient broadcasting with guaranteed coverage in mobile ad hoc networks
We study an efficient broadcast scheme in mobile ad hoc networks (MANETs). The objective is to determine a small set of forward nodes to ensure full coverage. We first study several methods that guarantee coverage when the local view of each node on its neighborhood information is updated in a timely manner. Then we consider a general case where nodes move even during the broadcast process, making it impractical to maintain up-to-date and consistent local views. A formal framework is used to model inaccurate local views in MANETs, where full coverage is guaranteed if three sufficient conditions, connectivity, link availability, and consistency, are met. Three solutions are proposed to satisfy those conditions. First, we give a minimal transmission range that maintains the connectivity of the virtual network constructed from local views. Then, we use two transmission ranges, one for neighborhood information collection and the other for actual data transmission, to form a buffer zone that guarantees the availability of logical links in the physical network. Finally, we propose a mechanism called aggregated local view to ensure consistent local views. By these, we extend Wu and Dai's coverage condition for broadcasting in a network with mobile nodes. The effectiveness of the proposed scheme is confirmed via both performance analysis and simulation study.
5787542
Relaxed game chromatic number of trees and outerplanar graphs
Abstract This paper studies the relaxed game chromatic number of trees and outerplanar graphs. It is proved that if G is a tree then χ g d ( G )⩽2 for d ⩾2. If G is an outerplanar graph, then χ g d ( G )⩽5 for d ⩾2, and χ g d ( G )⩾3 for d ⩽4.