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The flower snark is one of 6 snarks on 20 vertices.
The flower snark is one of 6 snarks on 20 vertices.

In graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In Mathematics and Computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects Graph theory is a growing area in mathematical research and has a large specialized vocabulary In the mathematical field of Graph theory, a cubic graph is a graph where all vertices are incident to exactly three edges In Graph theory, edge coloring is one type of the Graph coloring problem In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by three colors without two edges of the same color meeting at a point.

P. G. Tait initiated the study of snarks in 1880, when he proved that the four color theorem is equivalent to the statement that no snark is planar. Peter Guthrie Tait ( April 28, 1831 - July 4, 1901) was a Scottish mathematical physicist, best known for the seminal energy The four color theorem (also known as the four color map theorem) states that given any plane separated into regions such as a political map of the states of a country Kuratowski's and Wagner's theorems The Polish mathematician Kazimierz Kuratowski provided a characterization of planar graphs in terms of Forbidden The first known snark was the Petersen graph, discovered in 1898. In Graph theory, the Petersen graph is an Undirected graph with 10 vertices and 15 edges In 1946, Danilo Blanuša discovered two more snarks, and in 1975 Isaacs generalized Blanuša's method to construct an infinite family of snarks. Danilo Blanuša ( December 7 1903 &ndash August 8 1987) was a Croatian mathematician physicist engineer and a Professor Snarks were so named by the American mathematician Martin Gardner in 1976, after the mysterious and elusive object of the poem The Hunting of the Snark by Lewis Carroll. Martin Gardner (b October 21, 1914, Tulsa Oklahoma) is a popular American mathematics and science writer specializing in Recreational mathematics " The Hunting of the Snark (An Agony in 8 Fits " is a nonsense Poem written by Lewis Carroll (Charles Lutwidge Dodgson in 1874 when he was 42 years Charles Lutwidge Dodgson (ˈdɒdsən (27 January 1832 &ndash 14 January 1898 better known by the Pen name Lewis Carroll (/ˈkærəl/ was an English

In 2001, Robertson, Sanders, Seymour, and Thomas announced a proof of W. T. Tutte's conjecture that every snark has the Petersen graph as a minor, using an extension of a proof for the four color theorem. G Neil Robertson is a mathematician working mainly in Topological graph theory, currently a distinguished professor at The Ohio State University. Paul D Seymour (born July 26, 1950) is a mathematician working in Discrete mathematics, including Combinatorics, Graph theory William Thomas Tutte ( May 14 1917 &ndash May 2 2002) was a British, later Canadian codebreaker In Graph theory, a graph H is called a minor of the graph G if H is isomorphic to a graph that can be obtained by zero or more edge

List of snarks

References

External links

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