Related papers: Transitive cornerations in maps

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial…

A {\em kernel by properly colored paths} of an arc-colored digraph $D$ is a set $S$ of vertices of $D$ such that (i) no two vertices of $S$ are connected by a properly colored directed path in $D$, and (ii) every vertex outside $S$ can…

We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in the form of a compact, oriented surface…

Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a special kind of simple drawings that we call generalized…

A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the…

A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the…

We call an oriented odd cycle alternating if it has exactly one vertex whose in-degree and out-degree are both positive. In this paper, we investigate whether certain graphs admit an orientation that avoids alternating odd cycles as…

A detour in a graph is a longest path. This thesis is mainly about connected, non-traceable graphs with the property that each vertex is the start (or end) vertex of a detour. There are also related results on claw-free, 2-connected,…

A geometric graph is a drawing of a graph in the plane where the vertices are drawn as points in general position and the edges as straight-line segments connecting their endpoints. It is plane if it contains no crossing edges. We study…

For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.

An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…

A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along…

In studying properties of simple drawings of the complete graph in the sphere, two natural questions arose for us: can an edge have multiple segments on the boundary of the same face? and is each face the intersection of sides of 3-cycles?…

This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…

We consider the number of crossings in a graph which is embedded randomly on a convex set of points. We give an estimate to the normal distribution in Kolmogorov distance which implies a convergence rate of order $n^{-1/2}$ for various…

We show that a closed orientable 3--dimensional manifold admits a round fold map into the plane, i.e. a fold map whose critical value set consists of disjoint simple closed curves isotopic to concentric circles, if and only if it is a graph…

In this expository paper we present some ideas of algebraic topology (more precisely, of homology theory) in a language accessible to non-specialists in the area. A $1$-cycle in a graph is a set $C$ of edges such that every vertex is…

For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices. It is known from D\'enes' results that the permutation of a tree is a full cyclic…

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…