41020572
Cycle Partitions in Graphs
In this paper, we prove that every graph contains a cycle intersecting all maximum independent sets. Using this, we further prove that every graph with stability number α is spanned by α disjoint cycles. Here, the empty set, the graph of order 1 and the path of order 2 are all considered as degenerate cycles.
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.
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.
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.
45692912
Triangle-Free Graphs with Large Degree
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).
7571930
Using CBIR and pathfinder networks for image database visualisation
Digital images and videos have an increasingly important role in today's telecommunication and our everyday life in modern information society. In this paper, we explore the synergy between content-based image retrieval (CBIR) techniques and Pathfinder networks. Salient image features, based on colour, texture, edge orientation, and edge distance, are extracted. The structural modelling capabilities of Pathfinder are then applied to simplify and visualise the strongest interrelationships in the image database.
9048744
Web-based simulation experiments
The use of the World Wide Web and Java-based mobile code provides new opportunities for distributed simulation. First, the infrastructure provided by the Internet eliminates the need for multiprocessor hardware, making it feasible to distribute simulation models over different hardware platforms through the Internet. Second, "Internet-aware" mobile Java code makes the applications fully portable and reusable. These enabling technologies are already exploited for distributed simulation modeling. This paper reports on the preliminary results of an on-going effort to construct a parallel discrete event simulation support system to distribute simulation experiments over the Internet with a view on simulation optimization. A research prototype for ranking and selection problems is described. The overall project goals are discussed.
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}.
204988011
A class of additive multiplicative graph functions
For a fixed graph G, the capacity function for G, Po, is defined by Pc(H)= lim,__,®[yo(H')] TM, where y6(H) is the maximum number of disjoint G's in H. In [2], Hsu proved that Pr2 can be viewed as a lower bound for multiplicative increasing graph functions. But it was not known whether Pr2 is multiplicative or not. In this paper, we prove that Pc is multiplicative and additive for some graphs G which include K2. Some properties of Pc are also discussed in this paper.
12098402
Noise-aware repeater insertion and wire-sizing for on-chip interconnect using hierarchical moment-matching
Recently, several algorithms for interconnect optimization via repeater insertion and wire sizing have appeared based on the Elmore delay model. Using the Devgan noise metric a noise-aware repeater insertion technique has also been proposed recently. Recognizing the conservatism of these delay and noise models, we propose a moment-matching based technique to interconnect optimization that allows for much higher accuracy while preserving the hierarchical nature of Elmore-delay-based techniques. We also present a novel approach to noise computation that accurately captures the effect of several attackers in linear time with respect to the number of attackers and wire segments. Our practical experiments with industrial nets indicate that the corresponding reduction in error afforded by these more accurate models justifies this increase in runtime for aggressive designs which is our targeted domain. Our algorithm yields delay and noise estimates within 5% of circuit simulation results.