32173892
Note on Whitney's Theorem for k-connected Graphs
3744350
Hamiltonian graphs involving neighborhood unions
Dirac proved that a graph G is hamiltonian if the minimum degree δ(G) ≥ n/2, where n is the order of G. Let G be a graph and A ⊆ V(G). The neighborhood of A is N(A) = {b : ab ∈ E(G) for some a ∈ A}. For any positive integer k, we show that every (2k − 1)-connected graph of order n ≥ 16k is hamiltonian if |N(A)| ≥ n/2 for every independent vertex set A of k vertices. The result contains a few known results as special cases. The case of k = 1 is the classic result of Dirac when n is large and the case of k = 2 is a result of Broersma, Van den Heuvel, and Veldman when n is large. For general k, this result improves a result of Chen and Liu. The lower bound 2k − 1 on connectivity is best possible in general while the lower bound 16k for n is conjectured to be unnecessary. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 83–100, 2006
9764979
Tough enough chordal graphs are Hamiltonian
43538481
Vertex-disjoint cycles containing specified vertices in a bipartite graph
A minimum degree condition is given for a bipartite graph to contain a 2-factor each component of which contains a previously specified vertex. 2004 Wiley Periodicals, Inc. J Graph Theory 46: 145–166, 2004
3811952
Degree Sequences with Repeated Values
A given nonincreasing sequence D = (d1, d2, · · · , dn) is said to contain a (nonincreasing) repetition sequence D∗ = (di1 , di2 , · · · , dik ) for some k ≤ n − 2 if all values of D −D∗ are distinct and for any dil ∈ D ∗ there exists some dt ∈ D −D∗ such that dil = dt. For any pair of integers n and k with n ≥ k + 2, we investigate the existence of a graphic sequence which contains a given repetition sequence. Our main theorem contains the known results for the special case di1 = dik if k = 1 or k = 2 (see [1, 5, 2]). 1supported in part by a foundation of Academia Sinica.
39660968
A special k-coloring for a connected k-chromatic graph
For each positive integer k we consider the smallest positive integer f(k) (dependent only on k) such that the following holds: Each connected graph G with chromatic number ?(G) = k can be properly vertex colored by k colors so that for each pair of vertices xo and xp in any color class there exist vertices x1, x2, ?, xp-1 of the same class with dist(xi, xi+1) ? f(k) for each i, 0 ? i ? p ? 1. Thus, the graph is k-colorable with the vertices of each color class placed throughout the graph so that no subset of the class is at a distance > f(k) from the remainder of the class.We prove that f(k) < 12k when the order of the graph is ? k(k ? 2) + 1.
6529300
Compiler-guided data compression for reducing memory consumption of embedded applications
Memory system presents one of the critical challenges on embedded system design and optimization. This is mainly due to ever-increasing code complexity of embedded applications and exponential increase witnessed in the amount of data they manipulate. As a result, reducing memory space occupancy of embedded applications is very important and is even more important in the next decade. Motivated by this observation, this paper presents and evaluates a compiler-driven approach to data compression for reducing memory space occupancy. Our goal in this paper is to study how automated compiler support can help in deciding the set of data elements to compress/decompress and the points during execution at which these compressions/decompressions should be performed. The proposed compiler support achieves this by analyzing the source code of the application to be optimized and identifying the order in which the different data blocks are accessed. Based on this analysis, the compiler then automatically inserts compression/decompression calls in the application code. The compression calls target the data blocks that are not expected to be used in the near future, whereas the decompression calls target those data blocks with expected reuse but currently in compressed form.
30915392
An HCI method to improve the human performance reduced by local-lag mechanism
Local-lag mechanism can maintain consistency for replicated continuous applications, but with a tradeoff of adding delay to local operations. To relieve the negative effects of the delay, this paper proposes an HCI method named echo. With the help of the echo method users can immediately perceive the results of their operations and how large the lag is. In order to evaluate the proposed method, a desktop collaborative virtual environment (CVE) system and a virtual object control task were employed to study the effects of the echo method on human performance (including task completion time, error count, and interaction quality). Experimental results indicate that when the lag exceeds 100ms the echo method can improve human performance with the effects becoming more evident when a larger lag is used.
206570229
Graphs with Linearly Bounded Ramsey Numbers
Abstract A graph G of order n is p -arrangeable if its vertices can be ordered as v 1 , v 2 , ..., v n such that | N L i ( N Ri ( v i ))| ≤ p for each 1 ≤ i ≤ n − 1, where L i = { v 1 , v 2 , ..., v i }, R i = { v i +1 , v i +2 , ..., v n }, and N A ( B ) denotes the neighbors of B which lie in A . We prove that for each p ≥ 1, there is a constant c (depending only on p ) such that the Ramsey number r ( G , G ) ≤ cn for each p -arrangeable graph G of order n . Further we prove that there exists a fixed positive integer p such that all planar graphs are p -arrangeable.
8895078
An Adaptive-Filtering Policy for Distributed Virtual Environments
In this paper, an adaptive-filtering policy for distributed virtual environments (DVEs) was brought forward. It took advantages of two traditional filtering policies (static-filtering policy and equidistance-transmission policy) and could adaptively select the fittest filtering policy corresponding to current motion characteristic of the virtual object in DVEs. An experiment was designed to compare this filtering policy with the two traditional filtering policies on task performance. Objective (task completion time, state updates transmitted and state updates per second) and subjective (filtering quality) evaluations were recorded in the experiment. The experiment results show that if mean state updates per second is equal or greater than 20 in the task, SUT and SUPS can be decreased by adaptive-filtering policy without task performance affected obviously. However, if mean state updates per second is around 10 in the task, accompanied with SUT and SUPS decreased by adaptive-filtering policy, task performance also deteriorated badly
5706395
Combinatorial Properties of Generalized Hypercube Graphs
This paper investigates combinatorial properties of generalized hypercube graphs including best containers, wide diameter, and fault diameter. These properties have received much attention recently in the study of interconnection networks.