We study the threshold for the existence of a spanning maximal planar subgraph in the random graph Gn . We show that it is very near p = ~TTOWe also discuss the threshold for the existence of a spanning maximal outerplanar subgraph. This is very near

A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.

Maximal planar graphs embed in the euclidean plane as plane triangulations. Two such plane triangulations are equivalent if there is a homeomorphism of the plane which maps the vertices, edges and faces of one onto the corresponding elements of the other. A diagonal operation on a plane triangulation deletes an appropriate edge and inserts a related edge. We prove constructively that, given any...

We show that the kite graph $K_4^{(n)}$ uniquely maximizes distance spectral radius among all connected $4$-chromatic planar graphs on $n$ vertices.

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...

Abstract. The poset of noncrossing partitions can be naturally defined for any finite Coxeter group W . It is a self-dual, graded lattice which reduces to the classical lattice of noncrossing partitions of {1, 2, . . . , n} defined by Kreweras in 1972 when W is the symmetric group Sn, and to its type B analogue defined by the second author in 1997 when W is the hyperoctahedral group. We give a ...