Primitive spatial graphs and graph minors.
Problèmes ouverts. Représentation graphique d'un graphe
Quadrilateral embeddings of the conjunction of graphs
Quantized dual graded graphs.
Radial level planarity testing and embedding in linear time.
Reconstructing Surface Triangulations by Their Intersection Matrices 26 September 2014
The intersection matrix of a simplicial complex has entries equal to the rank of the intersecction of its facets. We prove that this matrix is enough to define up to isomorphism a triangulation of a surface.
Rectilinear Planar Layouts and Bipolar Orientations of Planar Graphs.
Recurrence of distributional limits of finite planar graphs.
Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4
We describe how the simple planar quadrangulations with vertices of degree 3 and 4, whose duals are known as octahedrites, can all be obtained from an elementary family of starting graphs by repeatedly applying two expansion operations. This allows for construction of a linear time generator of all graphs in the class with at most a given order, up to isomorphism.
Relating different cycle spaces of the same infinite graph.
Remark about a construction of some tournaments points of certain projective planes
Remarks on diagonalizable embeddings of graphs
Representing of K13 as a 2-pire map on the Klein bottle.
Rotary hypermaps of genus 2.
Sachs triangulations, generated by dessins d'enfant, and regular maps
Self-dual planar hypergraphs and exact bond percolation thresholds.
Self-dual regular maps from medial graphs.
Semi-topological classification of line patterns in the plane
Sharp edge-homotopy on spatial graphs.
A sharp-move is known as an unknotting operation for knots. A self sharp-move is a sharp-move on a spatial graph where all strings in the move belong to the same spatial edge. We say that two spatial embeddings of a graph are sharp edge-homotopic if they are transformed into each other by self sharp-moves and ambient isotopies. We investigate how is the sharp edge-homotopy strong and classify all spatial theta curves completely up to sharp edge-homotopy. Moreover we mention a relationship between...
Short cycles of low weight in normal plane maps with minimum degree 5
In this note, precise upper bounds are determined for the minimum degree-sum of the vertices of a 4-cycle and a 5-cycle in a plane triangulation with minimum degree 5: w(C₄) ≤ 25 and w(C₅) ≤ 30. These hold because a normal plane map with minimum degree 5 must contain a 4-star with . These results answer a question posed by Kotzig in 1979 and recent questions of Jendrol’ and Madaras.