169 research outputs found
Hamiltonian cycles through prescribed edges of 4-connected maximal planar graphs
AbstractIn 1956, W.T. Tutte proved that every 4-connected planar graph is hamiltonian. Moreover, in 1997, D.P. Sanders extended this to the result that a 4-connected planar graph contains a hamiltonian cycle through any two of its edges. It is shown that Sandersâ result is best possible by constructing 4-connected maximal planar graphs with three edges a large distance apart such that any hamiltonian cycle misses one of them. If the maximal planar graph is 5-connected then such a construction is impossible
Finding the Maximal Independent Sets of a Graph Including the Maximum Using a Multivariable Continuous Polynomial Objective Optimization Formulation
We propose a multivariable continuous polynomial optimization formulation to find arbitrary maximal independent sets of any size for any graph. A local optima of the optimization problem yields a maximal independent set, while the global optima yields a maximum independent set. The solution is two phases. The first phase is listing all the maximal cliques of the graph and the second phase is solving the optimization problem. We believe that our algorithm is efficient for sparse graphs, for which there exist fast algorithms to list their maximal cliques. Our algorithm was tested on some of the DIMACS maximum clique benchmarks and produced results efficiently. In some cases our algorithm outperforms other algorithms, such as cliquer
(Total) Vector Domination for Graphs with Bounded Branchwidth
Given a graph of order and an -dimensional non-negative
vector , called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
such that every vertex in (resp., in ) has
at least neighbors in . The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the -tuple dominating set problem (this is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto , where is the size of solution.Comment: 16 page
Large scale genome assemblies of Magnaporthe oryzae rice isolates from Italy
We report long-range sequencing of nine rice-infecting Magnaporthe oryzae isolates from different rice-growing regions of Italy using Oxford Nanopore Technology. We aquired chromosome-level genome assemblies, polished with Illumina short reads, and removed mitochondrial sequences to improve the quality of the assemblies.We provide the genome assemblies to the public with open access
Minimal vertex covers on finite-connectivity random graphs - a hard-sphere lattice-gas picture
The minimal vertex-cover (or maximal independent-set) problem is studied on
random graphs of finite connectivity. Analytical results are obtained by a
mapping to a lattice gas of hard spheres of (chemical) radius one, and they are
found to be in excellent agreement with numerical simulations. We give a
detailed description of the replica-symmetric phase, including the size and the
entropy of the minimal vertex covers, and the structure of the unfrozen
component which is found to percolate at connectivity . The
replica-symmetric solution breaks down at . We give a simple
one-step replica symmetry broken solution, and discuss the problems in
interpretation and generalization of this solution.Comment: 32 pages, 9 eps figures, to app. in PRE (01 May 2001
Status of the âMangrove tunicateâ Ecteinascidia turbinata (Ascidiacea: Perophoridae) in the Mediterranean Sea
The ascidian Ecteinascidia turbinata is reported from Maltese waters for the first time. Mature colonies were recorded on artificial substrata at two different sites (and on natural substrata at one of these), 4 km apart, during the summer months. The appearance of this ascidian is expected to be seasonal as the winter temperature in Malta may fall below that required for the maintenance of zooid growth. A second species, E. moorei, which was described in 1890 is here confirmed to be the same as E. turbinata, meaning that the species has existed in the Mediterranean since at least ~1880. The possibility that the Mediterranean population is a relic one from warmer periods cannot yet be excluded, so it is best described as being cryptogenic. The species appears to be spreading slowly, perhaps as a result of the rise in surface sea temperature. The Maltese sites offer an opportunity to monitor the species as they are accessible dive sites. This will allow assessment of whether this species remains restricted to these sites, or if it spreads perhaps to impact other species
Nonrepetitive Colouring via Entropy Compression
A vertex colouring of a graph is \emph{nonrepetitive} if there is no path
whose first half receives the same sequence of colours as the second half. A
graph is nonrepetitively -choosable if given lists of at least colours
at each vertex, there is a nonrepetitive colouring such that each vertex is
coloured from its own list. It is known that every graph with maximum degree
is -choosable, for some constant . We prove this result
with (ignoring lower order terms). We then prove that every subdivision
of a graph with sufficiently many division vertices per edge is nonrepetitively
5-choosable. The proofs of both these results are based on the Moser-Tardos
entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek
for the nonrepetitive choosability of paths. Finally, we prove that every graph
with pathwidth is nonrepetitively -colourable.Comment: v4: Minor changes made following helpful comments by the referee
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