Search results
Results from the WOW.Com Content Network
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, a professor of computer science at DePaul University , and published in 2018 by the CRC Press in their book series Discrete Mathematics and its Applications.
Richard Rado FRS [1] (28 April 1906 – 23 December 1989) was a German-born British mathematician whose research concerned combinatorics and graph theory. He was Jewish and left Germany to escape Nazi persecution. [2] He earned two PhDs: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge.
A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Chudnovsky's contributions to graph theory include the proof of the strong perfect graph theorem (with Neil Robertson, Paul Seymour, and Robin Thomas) characterizing perfect graphs as being exactly the graphs with no odd induced cycles of length at least 5 or their complements.
Thus we can find a graph with at least e − cr(G) edges and n vertices with no crossings, and is thus a planar graph. But from Euler's formula we must then have e − cr(G) ≤ 3n, and the claim follows. (In fact we have e − cr(G) ≤ 3n − 6 for n ≥ 3). To obtain the actual crossing number inequality, we now use a probabilistic argument.
A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar (can be drawn without crossings in the plane) if and only if it does not contain either of two forbidden graphs, the complete graph K 5 and the complete bipartite graph K 3,3.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
This graph has circuit rank r = 2 because it can be made into a tree by removing two edges, for instance the edges 1–2 and 2–3, but removing any one edge leaves a cycle in the graph. In graph theory, a branch of mathematics, the circuit rank, cyclomatic number, cycle rank, or nullity of an undirected graph is the minimum number of edges ...