2,192 research outputs found
The genus distribution of cubic graphs and asymptotic number of rooted cubic maps with high genus
Let be the number of rooted cubic maps with vertices on the
orientable surface of genus . We show that the sequence
is asymptotically normal with mean and variance asymptotic to
and , respectively. We derive an asymptotic expression for
when lies in any closed subinterval of . Using
rotation systems and Bender's theorem about generating functions with
fast-growing coefficients, we derive simple asymptotic expressions for the
numbers of rooted regular maps, disregarding the genus. In particular, we show
that the number of rooted cubic maps with vertices, disregarding the
genus, is asymptotic to
Brief introduction to tropical geometry
The paper consists of lecture notes for a mini-course given by the authors at
the G\"okova Geometry \& Topology conference in May 2014. We start the
exposition with tropical curves in the plane and their applications to problems
in classical enumerative geometry, and continue with a look at more general
tropical varieties and their homology theories.Comment: 75 pages, 37 figures, many examples and exercise
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
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