6880798
Graphs with Hamiltonian cycles having adjacent lines different colors
Let G be a complete graph Kp (or a complete bipartite graph Km,m) with its lines colored so that no point is on more than k lines of the same color. If p ≥ 17k (or m ≥ 25k) then G has a cycle of every possible size with adjacent lines different colors.
45692912
Triangle-Free Graphs with Large Degree
19946044
On edge-Hamiltonian property of Cayley graphs
Abstract Let G be a group generated by X . A Cayley graph over G is defined as a graph G ( X ) whose vertex set is G and whose edge set consists of all unordered pairs [ a,b ] with a , b ϵ G and a -1 b ϵ X ∩ X -1 , where X -1 denotes the set { x -1 ∣ x ϵ X }. When X is a minimal generating set or each element of X is of even order, it can be shown that G ( X ) is Hamiltonian if it is edge-Hamiltonian. Hence every Cayley graph of order a power of 2 is edge-Hamiltonian.
18457324
On the higher-order edge toughness of a graph
For an integer c, 1?c??V(G)??1, we define the cth-order edge toughness of a graph G as tc(G)=min|X|?(G?X)?cX?E(G) & ?(G?X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughness ?c(G) of a graph G, we prove that `?c(G)?k if and only if G has k edge-disjoint spanning forests with exactly c components?. We also study the `balancity? of a graph G of order p and size q, which is defined as the smallest positive integer c such that ?c(G) = p/(p?c).
28223559
Constructions of point-colour-symmetric graphs
Throuhout this paper, we shall restrict ourselves to finite graphs G which are undirected and line-coloured. For any points x, y in G, we shall write x y to mean that x and y are adjacent and by x w1 y to mean that x y and the colour of the line joining x and y is i. Also, we shall denote the line joining x and y by Xy; the colour of Xy by c(xy); and the set {c(Xy)l x y in Gl by C(G). Let G and H be (undirected, line-coloured) graphs. A one to one mapping ffrom G onto His called an isomorphism if the following two conditions are satisfied:
20073710
On a class of Hamiltonian laceable 3-regular graphs
Abstract Using the concept of brick-products, Alspach and Zhang showed in Alspach and Zhang (1989) that all cubic Cayley graphs over dihedral groups are Hamiltonian. It is also conjectured that all brick-products C(2n, m, r) are Hamiltonian laceable, in the sense that any two vertices at odd distance apart can be joined by a Hamiltonian path. In this paper, we shall study the Hamiltonian laceability of brick-products C(2n, m, r) with only one cycle (i.e. m = 1). To be more specific, we shall provide a technique with which we can show that when the chord length r is 3, 5, 7 or 9, the corresponding brick-products are Hamiltonian laceable. Let s = gcd((r + 1)/2, n) and t = gcd((r − 1)/2, n). We then show that the brick-product C(2n, 1, r) is Hamiltonian laceable if (i) st is even; (ii) s is odd and rs  r + 1 + 3s (mod 4n); or (iii) t is odd and rt  r − 1 − 3t (mod 4n). In general, when n is sufficiently large, say n ⩾ r2 − r + 1, then the brick-product is also Hamiltonian laceable.
2867815
Matchings and matching extensions in graphs
Abstract Let G be a graph with a perfect matching and k be an integer such that 1 ⩽ k vbV ( G ) vb /2. Then G is said to be k -extendable if every matching of size k in G extends to a perfect matching of G . Plummer (1994) proved that every (2 k + 1)-connected K 1,3 -free graph of even order is k -extendable. In this paper, it was proved that every (2 k + n − 2)-connected K 1, n -free graph of even order is k -extendable. Also, an answer to the problem of characterizing maximal k -extendable graphs posted by Plummer (1994) and Saito (1989/90) is given. Besides, we show that a regular graph of even order belongs to the first class if its any two odd cycles have at least a vertex in common.
2365001
Bridging the Gap: The Use of Pathfinder Networks in Visual Navigation
Abstract This paper describes a generic approach to the design of a 3D virtual environment for visual navigation. The basic design principle is that users need to understand how an environment is organised and how they can utilise the knowledge to find their way through the environment. In this paper, we focus on the relationship between implicit semantic structures associated with a collection of domain-specific documents and users' cognitive needs in the context of visual navigation. We extend the notion of Pathfinder networks in order to represent implicit semantic structures in a 3D virtual environment. Users' cognitive needs in visual navigation are conceptualised based on the concept of cognitive maps.
29297649
Shape from Photometric Stereo and Contours
In this work, we propose an alternative approach to 3D shape recovery by combining photometric stereo and shape from contours methods. Surfaces recovered by photometric stereo are aligned, adjusted and merged according to a preliminary 3D model obtained by shape from contours. Comparisons are conducted to evaluate the performances of different methods. It has been found that the proposed approach provides more accurate shape recovery than the photometric stereo and shape from contours methods.
18159266
A Distributed Simulation-Based Computational Intelligence Algorithm for Nanoscale Semiconductor Device Inverse Problem
In this paper, a distributed simulation-based computational intelligence algorithm for inverse problem of nanoscale semiconductor device is presented. This approach features a simulation-based optimization strategy, and mainly integrates the semiconductor process simulation, semiconductor device simulation, evolutionary strategy, and empirical knowledge on a distributed computing environment. For a set of given target current-voltage (I-V) curves of metal-oxide-semiconductor field effect transistors (MOSFETs) devices, the developed prototype executes evolutionary tasks to solve an inverse doping profile problem, and therefore optimize fabrication recipes. In the evolutionary loop, the established management server allocates the jobs of process simulation and device simulation on a PC-based Linux cluster with message passing interface (MPI) libraries. Good benchmark results including the speed-up, the load balancing, and the parallel efficiency are presented. Computed results, compared with the realistic measured data of 65 nm n-type MOSFET, show the accuracy and robustness of the method.
27005423
Binding number and toughness for matching extension
Abstract A graph G of even order is said to be k -extendable if every matching of size k in G can be extended to a 1-factor of G . Plummer (1988) showed that a graph G is k -extendable if tough ( G ) > k , and we here prove that G is also k -extendable if bind ( G ) > max {k, (7k + 13)/12}.