
...let c(g) denote the number of simple cycles of a graph g and let c(n) be the maximum of c(g) over all planar graphs with n nodes. we present...


...we investigate the maximum number of simple cycles and the maximum number of hamiltonian cycles in a planar graph g with n vertices. using...is an upper bound for the number of hamiltonian cycles. moreover, we obtain upper bounds for the number of simple cycles
of a given length with a...

...finding any fixed subgraph h in a given nvertex planar graph [5], the multiplication constant hidden in “o” notation (which depends on the size of h) is so high, that...implement.
as a sideeffect of our approach we show that the maximum number of kcycles in nvertex planar graph is
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...nn) space for enumerating all simple cycles of a planar graph with n vertices, where α is the total number of simple cycles in the graph unlike backtrack algorithms, cycle vector space algorithms for this...

...known to be npcomplete. in this paper, we give a number of simple data reduction rules. each rule transforms
the input to an equivalent smaller...carried out have size linear in k. thereby we obtain that the k
disjoint cycles problem on planar graphs has a kernel of linear size. we also present...

...extended,to a venn diagram,of n+1 curves,by the,addition,of a suitable simple closed curve. 1., introduction:a,venn diagram,consists,of n simple,closed,curves inthe,plane,so...are nonempty and are connected.,one can put various restrictions on the diagrams and obtain specialclasses,of venn,diagrams,[4]. the exact definitions used in this paper are given in...

...transversal set that intersects all (simple) cycles of length at most s in a planar graph, where s ≥ 3 is a constant...size is an exponential improvement in terms of s over the kernel size obtained under the metakernelization framework by bodlaender et...

...subexponential exact and parameterized algorithms on planar graphs. our
approach is based on geometric properties of planar branch decompositions obtained by seymour...time algorithm solving weighted hamiltonian cycle on an nvertex planar graph. similar technique solves planar graph travelling salesman problem with n cities in time
. our approach can be...

...to many complexity results for planar graph problems. for exam ple, by using this approach, many planar graph problems can be solved in time 2o( p n) , where...design paradigm for solving problems on planar graphs. the paradigm is so simple that it can be explained in any textbook on graph algorithms: compute tree or branch...