The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...

the four color problem. It was generalised to the Tutte polynomial by Hassler Whitney and W. T. Tutte, linking it to the Potts model of statistical physics...

said to be a Tutte-Grothendieck invariant. The Tutte polynomial is the most general such invariant; that is, the Tutte polynomial is a Tutte-Grothendieck...

spanning trees, each consisting of a single one of these edges. The Tutte polynomial of a graph can be defined as a sum, over the spanning trees of the...

William Thomas Tutte OC FRS FRSC (/tʌt/; 14 May 1917 – 2 May 2002) was an English and Canadian code breaker and mathematician. During the Second World...

introduced the chromatic polynomial to study the coloring problem, which was generalised to the Tutte polynomial by W. T. Tutte, both of which are important...

perfect matching exists. (This polynomial is not the Tutte polynomial of G.) The Tutte matrix is named after W. T. Tutte, and is a generalisation of the...

later found that the flow polynomial is yet another; and soon Tutte discovered an entire class of functions called Tutte polynomials (originally referred to...

through their invariants, especially the colored Tutte polynomial, which generalizes the Tutte polynomial of a signed graph of Kauffman (1989). There has...

representations (e.g., given a graph G and two numbers x and y, does the Tutte polynomial TG(x,y) have a combinatorial interpretation?). Although there are very...

similar class of polynomial invariants in graph theory Tutte polynomial, a special type of graph polynomial related to the Jones polynomial Skein relation...

of integers, such as the degree sequence of a graph. A polynomial, such as the Tutte polynomial of a graph. Easily computable graph invariants are instrumental...

into two induced trees. If a planar graph G has Tutte polynomial TG(x,y), then the Tutte polynomial of its dual graph is obtained by swapping x and y...

Dominic (1999). "The Tutte polynomial". Random Structures & Algorithms. 15 (3–4). Goodall, Andrew (2008). "Graph polynomials and Tutte-Grothendieck invariants:...

result on evaluations of the Tutte polynomial at (3,3). For a plane graph G, n times the evaluation of the Tutte polynomial at the point (n+1,n+1) equals...

In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally...

reliability polynomial, a polynomial that describes the probability of remaining connected after independent edge failures The Tutte polynomial, a polynomial in...

quantum field theory. This includes work on the chromatic polynomial and the Tutte polynomial, which appear both in algebraic graph theory and in the study...

orientation of the dual graph and vice versa. Like the chromatic polynomial, the Tutte polynomial T G {\displaystyle T_{G}} of a graph G {\displaystyle G} ,...

minimum spanning tree can be calculated as an integral involving the Tutte polynomial of the graph. In contrast to uniformly random spanning trees of complete...

graphs, and especially the chromatic polynomial, the Tutte polynomial and knot invariants. The chromatic polynomial of a graph, for example, counts the...

{\displaystyle (x-4)(x-1)^{4}x^{2}(x+1)(x+3)^{2}(x^{2}+x-4)} . The Tutte polynomial of the Chvátal graph has been computed by Björklund et al. (2008)....

model is a specialization of the Tutte polynomial, which itself is a specialization of the multivariate Tutte polynomial. The parameter q {\displaystyle...

the Tutte polynomial. These polynomials were discovered by Béla Bollobás and Oliver Riordan (2001, 2002). The 3-variable Bollobás–Riordan polynomial of...

probabilistic polynomial identity testing. Identity testing is the problem of determining whether a given multivariate polynomial is the 0-polynomial, the polynomial...

property is not true, but the Hahn–Banach theorem nevertheless holds. The Tutte polynomial of the Vámos matroid is x 4 + 4 x 3 + 10 x 2 + 15 x + 5 x y + 15 y...

being connected. Tutte polynomial Characteristic polynomial Planarity The number of spanning trees in a graph Chromatic polynomial Being a perfect graph...

above results were proved by Tutte in 1953 when he was studying the Tutte polynomial, a generalization of the flow polynomial. There is a duality between...

The automorphism group of the Tutte graph is Z/3Z, the cyclic group of order 3. The characteristic polynomial of the Tutte graph is : ( x − 3 ) ( x 15 −...

through the model's relation to percolation problems and the Tutte and chromatic polynomials found in combinatorics. For integer values of q ≥ 3 {\displaystyle...