9764979
Tough enough chordal graphs are Hamiltonian
316842
Cycles in 4-connected planar graphs
Let G be a 4-connected planar graph on n vertices. Previous results show that G contains a cycle of length k for each k ∈ {n, n - 1,n - 2, n - 3} with k ≥ 3. These results are proved using the "Tutte path" technique, and this technique alone cannot be used to obtain further results in this direction. One approach to obtain further results is to combine Tutte paths and contractible edges. In this paper, we demonstrate this approach by showing that G also has a cycle of length k for each k ∈ {n - 4, n - 5, n - 6} with k ≥ 3. This work was partially motivated by an old conjecture of Malkevitch.
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.
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
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
45338790
Graphs with a Cycle of Length Divisible by Three
In this paper, we will prove that every graph G with minimum degree ?(G) ? 3 contains a cycle of length divisible by three. This was conjectured to be true by Barefoot, Clark, Douthett, and Entringer.
30765152
On the Quickest Path Problem
Abstract Let N be an input network and σ be the amount of data to be transmitted. We present an O( mn 2 ) time algorithm that finds all-pairs quickest paths, for a given value of σ, and show that the quickest path between any two nodes for any value of σ can be found in O(log m ) time, provided O( mn 2 ) preprocessing time is spent.
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.
14081
Memory-Conscious Reliable Execution on Embedded Chip Multiprocessors
Code and data duplication has been identified as one of the important mechanisms for improving reliability. In a chip multiprocessor-based execution environment, while it is possible to hide the overhead of code duplication through parallelism, hiding the memory space overhead incurred by data duplication is more difficult. This paper presents a compiler-directed memory-conscious data duplication scheme that tries to minimize the extra memory space required by duplicate execution. The proposed approach achieves this goal by using the memory locations that hold dead data to store the duplicates of the actively-used data. In this way, instead of using extra memory storage for duplicate elements, we use the existing memory locations to the extent allowed by usage patterns of data. The results collected from our experiments clearly show that the proposed approach saves significant memory space, as compared to a straightforward approach that implements full duplication
13431767
A compiler approach for reducing data cache energy
Silicon technology advances have made it possible to pack millions of transistors --- switching at high clock speeds --- on a single chip. While these advances bring unprecedented performance to electronic products, they pose difficult power/energy consumption problems. For example, large number of transistors in dense on-chip cache memories consume significant static (leakage) power even if the cache is not used by the current computation. While previous compiler research studied code and data restructuring for improving data cache performance, to our knowledge, there is no compiler-based study that targets data cache leakage power consumption. In this paper, we present code restructuring techniques for array-based and pointer-intensive applications for reducing data cache energy consumption. The idea is to let the compiler to analyze the code and insert instructions that turn off cache lines that keep variables not used by the current computation. This turning off does not destroy contents of a cache line, and waking up the cache line incurs very little overhead. Due to data locality, we find that at a given time only a small portion of the data cache needs to be active; the remaining part can be placed into a leakage-saving mode (state); i.e., they can be turned off. Our preliminary results indicate that the proposed strategy reduces the cache energy consumption significantly. We also show that several compiler optimizations increase the effectiveness of our strategy.
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.