Crossing Numbers of Graphs information

Crossing Numbers of Graphs is a book in mathematics, on the minimum number of edge crossings needed in graph drawings. It was written by Marcus Schaefer...

crossing). A topological graph is also called a drawing of a graph. An important special class of topological graphs is the class of geometric graphs...

planar graphs. However, every planar drawing of a complete graph with five or more vertices must contain a crossing, and the nonplanar complete graph K5 plays...

Saaty (1964) and Nicholson (1968), who used arc diagrams to study crossing numbers of graphs. An older but less frequently used name for arc diagrams is linear...

subset and a vertex in the other subset. Planar graphs are the graphs that can be drawn without crossings in the plane, and if such a drawing could be found...

drawing of a given graph, as a function of the number of edges and vertices of the graph. It states that, for graphs where the number e of edges is sufficiently...

known: the complete graph K2, the Petersen graph, the Coxeter graph and two graphs derived from the Petersen and Coxeter graphs by replacing each vertex...

Unsolved problem in mathematics: Do complete graphs have the smallest possible crossing number among graphs with the same chromatic number? (more unsolved...

subdivision of it), one of the Blanuša snarks, and all Möbius ladders are toroidal. More generally, any graph with crossing number 1 is toroidal. Some graphs with...

number of a graph G {\displaystyle G} is NP-hard. However, for certain classes of graphs, stronger results hold. For example, for planar graphs, determining...

which the graphs are arranged in concentric circles around some starting node and to three-dimensional layered drawings of graphs. In layered graph drawings...

complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are the subhamiltonian graphs, which...

extensions of the concept of a line graph have been studied, including line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs...

graphs, which are graphs that have exactly three edges touching each vertex. The only hypercube graph Qn that is a cubic graph is the cubical graph Q3...

theory of the real numbers with the exponential function decidable? The universality problem for C-free graphs: For which finite sets C of graphs does the...

undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or...

cyclic graph, but this term has other meanings. Circulant graphs can be described in several equivalent ways: The automorphism group of the graph includes...

number of crossings is zero only for outerplanar graphs. For other graphs, it may be optimized or reduced separately for each biconnected component of the graph...

signed graphs and gain graphs. Critical graph Graph coloring game Graph homomorphism Hajós construction Mathematics of Sudoku Multipartite graph Uniquely...

the mathematical field of graph theory, planarization is a method of extending graph drawing methods from planar graphs to graphs that are not planar, by...

distance-regular graph, is one of only 5 known connected vertex-transitive graphs with no Hamiltonian cycles. The automorphism group of the Petersen graph is the...

Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the 3-vertex-connected, planar graphs. The Schlegel diagram of a convex polyhedron...

multiple graphs on a shared vertex set into the plane so that all the graphs are drawn without crossings; recognizing the visibility graphs of planar point...