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.
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.
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
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
1039631
New Conditions for k-ordered Hamiltonian Graphs
We show that in any graph G on n vertices with d(x) + d(y) ≥ n for any two nonadjacent vertices x and y, we can fix the order of k vertices on a given cycle and find a hamiltonian cycle encountering these vertices in the same order, as long as k < n/12 and G is d(k + 1)/2e-connected. Further we show that every b3k/2cconnected graph on n vertices with d(x) + d(y) ≥ n for any two nonadjacent vertices x and y is k-ordered hamiltonian, i.e. for every ordered set of k vertices we can find a hamiltonian cycle encountering these vertices in the given order. Both connectivity bounds are best possible.
2166475
Temperature-sensitive loop parallelization for chip multiprocessors
In this paper, we present and evaluate three temperature-sensitive loop parallelization strategies for array-intensive applications executed on chip multiprocessors in order to reduce the peak temperature. Our experimental results show that the peak (average) temperature can be reduced by 20.9/spl deg/C (4.3/spl deg/C) when averaged over all the applications tested, incurring small performance/power penalties.
13046770
Local leader election, signal strength aware flooding, and routeless routing
We have identified a fundamental operator in wireless networks that we named the local leader election in which the goal is to select a node in a spatially close neighborhood. We present a simple and efficient solution to the local leader election problem by making use of both: (i) implicit synchronization points, commonly observable by all nodes in the same neighborhood, and (ii) the prioritized backoff delay, dependent on the desired probability of each node becoming a leader. We then show that both flooding and routing are instances of the local leader election problem, so our general solution naturally applies. By relating the backoff delay to the signal strength of the received packet, we have designed a variant of flooding named signal strength aware flooding (SSAF) that can improve its efficiency. By using a different metric to derive the backoff delay, we have designed a new generation wireless routing protocol, that we named the routeless routing protocol that possesses several interesting properties.
35779178
On the Quickest Path Problem
In this paper, we propose an O(mn2) time algorithm that finds all-pairs quickest paths in a given network N, where n and m are the numbers of nodes and arcs, respectively, in N. Besides, the quickest path between any two nodes can be determined in O(log m) time, provided O(mn2) time preprocessing is made.
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.
1780811
Reducing code size through address register assignment
In DSP processors, minimizing the amount of address calculations is critical for reducing code size and improving performance, since studies of programs have shown that instructions that manipulate address registers constitute a significant portion of the overall instruction count (up to 55%). This work presents a compiler-based optimization strategy to “reduce the code size in embedded systems.” Our strategy maximizes the use of indirect addressing modes with postincrement/decrement capabilities available in DSP processors. These modes can be exploited by ensuring that successive references to variables access consecutive memory locations. To achieve this spatial locality, our approach uses both access pattern modification (program code restructuring) and memory storage reordering (data layout restructuring). Experimental results on a set of benchmark codes show the effectiveness of our solution and indicate that our approach outperforms the previous approaches to the problem. In addition to resulting in significant reductions in instruction memory (storage) requirements, the proposed technique improves execution time.