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
8564003
Ramsey Problems Involving Degrees in Edge-colored Complete Graphs of Vertices Belonging to Monochromatic Subgraphs
We consider monochromatic subragraphs in two-colored graphs as guaranteed by Ramsey's theorem, and ask various questions concerning the degree in the two-colored complete graphs of vertices which are part of these subgraphs.
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
9440735
Graph minors and linkages
Bollobás and Thomason showed that every 22k-connected graph is k-linked. Their result used a dense graph minor. In this paper we investigate the ties between small graph minors and linkages. In particular, we show that a 6-connected graph with a K− 9 minor is 3-linked. Further, we show that a 7-connected graph with a K− 9 minor is (2, 5)-linked. Finally, we show that a graph of order n and size at least 7n − 29 contains a K−− 9 minor.
15455231
Long Cycles in 3-Connected Graphs
Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Ω(nlog32). In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the projective plane, or the torus, or the Klein bottle.
2371887
Locality-conscious process scheduling in embedded systems
In many embedded systems, the existence of a data cache might influence the effectiveness of process scheduling policy significantly. Consequently, a scheduling policy that takes inter-process data reuse into account might result in large performance benefits. In this paper, we focus on array-intensive embedded applications and present a locality-conscious scheduling strategy where we first evaluate the potential data reuse between processes, and then, using the results of this evaluation, select an order for process executions. We also show how process codes can be transformed by an optimizing compiler for increasing inter-process data reuse, thereby making locality-conscious scheduling more effective. Our experimental results obtained using two large, multi-process application codes indicate significant runtime benefits.
1469916
Entrapping adversaries for source protection in sensor networks
Sensor networks are used in a variety of application areas for diverse problems from habitat monitoring to military tracking. Whenever they are used to monitor sensitive objects, the privacy of monitored objects' locations becomes an important concern. When a sensor reports a monitored object by sending a series of messages through the sensor network, the route these messages take in theory creates a trail leading back to their source. By eavesdropping on communications, an attacker may be able to move from node to node to follow this trail. Several approaches aimed at discouraging this kind of eavesdropping have been proposed, including mechanisms for constructing "phantom" routes and approaches that insert fake sources as background noise. A problem with existing approaches is that message latencies become larger and energy costs become higher as a result of introducing protections for the privacy of a source location. This paper proposes a new cyclic entrapment method (CEM) that protects source locations in sensor networks while adding a comparatively low cost in terms of additional message latency and energy
17810541
An adaptive locality-conscious process scheduler for embedded systems
A critical component of a real-time operating system (RTOS) is its process scheduler. While the prior research on process scheduling focuses mostly on meeting hard/soft deadlines, preemption and priory assignment related issues, problems arise from existence of cache memories are largely ignored. Focusing on data accesses and a cache based embedded system, this paper proposes an adaptive locality-conscious process scheduling algorithm. The main goal of the proposed algorithm is to exploit (reuse) the contents of the on-chip cache memory to the highest extent possible. The algorithm tries to achieve its goal by determining the order in which the processes get scheduled such that the successively-executing processes share a large number of data elements. We implemented our scheduler within a customized simulation platform and simulated it using a set of benchmark codes. Our experimental results reveal that the proposed scheduling algorithm is very successful in practice, and reduces process completion times significantly for both rate-monotonic scheduling (RMS) and earliest-deadline-first scheduling (EDF). We also explain how process code transformations can be used for increasing the savings achieved by the locality-conscious scheduler, and show how the proposed approach operates with a base scheduler such as RMS and EDF.
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.
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.