One of the fundamental results in graph theory is the theorem of turan, proved. A short proof of turan s theorem mathematical association of. Turans theorem states that if g is a graph with n vertices such that. Let f be a graph that contains an edge whose deletion reduces its chromatic number. This proof makes use of the structure of the turan graphs. For a graph h and an integer, let be the minimum real number such that every partite graph whose. This theorem gives the best known upper bound for exn, c6. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Turan s theorem in the 1940s marked the birth of extremal graph theory.
Two vertices in the graph are adjacent exactly if they are not in the same part. Theorem of the day is registered as a uk trademark, no. In this article we derive a similar theorem for multipartite graphs. For such a graph f, a classical result of simonovits from 1966 shows that every graph on vertices with more than edges contains a copy of f. A pdf copy of the article can be viewed by clicking below. For example, jaguar speed car search for an exact match.
Observe that mantels theorem is a special case of the turan s theorem with r 2. What links here related changes upload file special pages permanent link page information wikidata item cite this page. Turan theorems and convexity invariants for directed graphs article in discrete mathematics 30820. Since the extremal example for the hajnalszemeredi theorem is very similar to. This theorem generalises a previous result by mantel 1907, which states that the maximum number of egdes in an nvertex trianglefree simple graph is bn24c. A kchromatic graph has a kvertex coloring, which can be. This quantity is called the turan number of f, and is denoted by exn. Tur an s theorem, zykovs theorem, and the n k r notation a tur an graph t n. On 3hypergraphs with forbidden 4vertex configurations people. Embedding problems and ramseyturan variations in extremal. X exclude words from your search put in front of a word you want to leave out. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page. We note that this proof yields the full statement els\eh, h turan graph. A graduatelevel introduction to modern graph theory through existential and algorithmic problems, and the corresponding.
On the minimal density of triangles in graphs people. The local geometry of graphs, or, how to read large graphs. A fast and provable method for estimating clique counts using turans theorem shweta jain university of california, santa cruz. Graph theory and additive combinatorics yufei zhao. Let me v with dm max sisad we denote by s the neighbors. On the turan number for the hexagon princeton math. Turan theorems and convexity invariants for directed graphs.