We review results concerning edge flips in planar graphs concentrating mainly on various
aspects of the following problem: Given two different planar graphs of the same size, how …

A realizer of a maximal plane graph is a set of three particular spanning trees. It has been
used in several graph algorithms and particularly in graph drawing algorithms. We propose …

The paper continues the consideration of Hilbert mathematics to mathematics itself as an
additional “dimension” allowing for the most difficult and fundamental problems to be …

This paper discusses reformulations of the problem of coloring plane maps with four colors.
We include discussion of the Eliahou–Kryuchkov conjecture, the Penrose formula, the vector …

One of the popular methods studied for indoor positioning is based on Wi‐Fi signal strength.
But distance decisions using signal strength show not only intuitive results but also irregular …

Let σ1, σ2 be two permutations in the symmetric group Sn. Among the many sequences of
elementary transpositions τ1,…, τr transforming σ1 into σ2= τr⋯ τ1σ1, some of them may be …

In this paper, we prove that any two triangulations of a given polygon may be transformed
into one another by a signable sequence of flips if and only if every planar graph is 4 …

The effective use of energy efficiency is a big challenge in sensor networks, since sensor
nodes have limited power and are deployed in inaccessible regions. Clustering on the …

Hassler Whitney's theorem of 1931 reduces the task of finding proper, vertex 4-colorings of
triangulations of the 2-sphere to finding such colorings for the class ℌ of triangulations of the …

The energy performance of sensor nodes which are deployed in arbitrary regions in sensor
networks is an important issue. Clustering of the network is a method to make nodes to …