30478531
Hamiltonian decompositions of Cayley graphs on Abelian groups
Abstract Alspach has conjectured that any 2k-regular connected Cayley graph cay(A,S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S={s1,s2,s3} is a minimal generating set of A with |A| odd, or S={s1,s2,…,sk} is a generating set of A such that gcd(ord(si),ord(sj))= 1 for i≠j.
33569862
Survey of Double Vertex Graphs
Abstract. Let G be a (V,E) graph of order p≥2. The double vertex graphU2(G) is the graph whose vertex set consists of all 2-subsets of V such that two distinct vertices {x,y} and {u,v} are adjacent if and only if |{x,y}∩{u,v}|=1 and if x=u, then y and v are adjacent in G. For this class of graphs we discuss the regularity, eulerian, hamiltonian, and bipartite properties of these graphs. A generalization of this concept is n-tuple vertex graphs, defined in a manner similar to double vertex graphs. We also review several recent results for n-tuple vertex graphs.
30471911
Hamiltonian Decompositions of Cayley Graphs on Abelian Groups of Odd Order
6169415
The Color-Degree Matrix and the Number of Multicolored Trees in Star Decompositions
In a previous paper we investigated the problem of counting the number of multicolored spanning trees in biclique decompositions. In particular for acyclic decompositions we found the minimum and maximum numbers of multicolored trees. We now introduce the color-degree matrix C and show that the number of multicolored trees is bounded below by the determinant of C with a row deleted. In fact, we obtain equality for acyclic decompositions and for star decompositions. Unfortunately, for arbitrary decompositions the ratio of this determinant to the actual number of trees can approach zero. We find that star decompositions on n vertices are in one to one correspondence with tournaments on n ? 1 vertices. This allows us to determine that the minimum number of multicolored trees among all star decompositions of Kn is (n ? 1)! and the average number is ((n + 1)/2)n ? 2. We bound the maximum number of multicolored trees between this average and ?n2/4?(n ? 1)/2 ? ?(n ? 2)2/4?(n ? 1)/2.
18277516
Mesh Optimisation Using Edge Information in Feature-Based Surface Reconstruction
One of the most challenging and fundamental problems in computer vision is to reconstruct a surface model given a set of uncalibrated 2D images. Well-established Structure from Motion (SfM) algorithms often result in a sparse set of 3D surface points, but surface modelling based on sparse 3D points is not easy. In this paper, we present a new method to refine and optimise surface meshes using edge information in the 2D images. We design a meshing – edge point detection – re-meshing scheme that can gradually refine the surface mesh until it best fits the true physical surface of the object being modelled. Our method is tested on real images and satisfactory results are obtained.
14178256
Distributed Problem Solving Without Communication - An Examination of Computationally Hard Satisfiability Problems
In this paper, we extend and modify the ERA approach proposed in Ref. 13 to solve Propositional Satisfiability Problems (SATs). The new ERA approach involves a multiagent system where each agent only senses its local environment and applies some self-organizing rules for governing its movements. The environment, which is a two-dimensional cellular environment, records and updates the local values that are computed and affected according to the movements of individual agents. In solving a SAT with the ERA approach, we first divide variables into several groups, and represent each variable group with an agent whose possible positions correspond to the elements in a Cartesian product of variable domains, and then randomly place each agent onto one of its possible positions. Thereafter, the ERA system will keep on dispatching agents to choose their movements until an exact or approximate solution emerges. The experimental results on some benchmark SAT test-sets have shown that the ERA approach can obtain comparable results as well as stable performances for SAT problems. In particular, it can find approximate solutions for SAT problems in only a few steps. The real value of this approach is that it is a distributed asynchronous approach without any centralized control or evaluation, where the agents can cooperate to solve problems without explicit communication.
14115714
Energy-efficient compressed address transmission
To realize energy-efficient buses in current nanometer-scale technologies, techniques like compression or encoding that exploit information redundancy have been explored. However, available compression techniques for buses do not always ensure energy-efficient transmission of compressed information. In this work, we present various techniques that can be used with compression schemes for buses to ensure high energy efficiency. Our best scheme, applied to a stream of 38-bit addresses issued in a typical microprocessor, yields about 14.7% energy reduction on the average across a wide range of compressed bus widths ranging and over many SPEC CPU2000 benchmarks. Our proposed techniques especially perform better - up to 28.8% energy reduction is obtained - for narrower bus widths in the range 8-16 bits.
12925025
The 4-Choosability of Plane Graphs without 4-Cycles'
A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosable.
46639086
Triangle-Free Circuit Decompositions and Petersen Minor
In this paper, we characterize those simple graphs with no Petersen minor which admit triangle-free circuit decompositions.