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practical for networks comprising more than a few dozen vertices. Although no polynomial time algorithm is known for this problem, more efficient algorithms than...

of q colors, called its chromatic polynomial, remains unknown so far. The scaling of zeros of the chromatic polynomial of random graphs with parameters...

theory), the cardinality of a group or period of an element Order of a polynomial (disambiguation) Order of a square matrix, its dimension Order (ring theory)...

number 3 and chromatic index 2n. Its chromatic polynomial can be deduced from the chromatic polynomial of the cycle graph C3 and is equal to ( x − 2 )...

problem cannot be solved efficiently (where efficiently typically means "in polynomial time"). It is not known how to prove (unconditional) hardness for essentially...

graphs have bounded expansion. A closely related but stronger property, polynomial expansion, is equivalent to the existence of separator theorems for these...

weight data points to sequentially reduce error. Polynomial chaos expansions, which use orthogonal polynomials to approximate the response surface. Smoothing...

combinatorics and probability theory. Arratia developed the ideas of interlace polynomials with Béla Bollobás and Gregory Sorkin, found an equivalent formulation...

theorems", is probably due to Alfréd Rényi, although it is often attributed to Rényi's colleague Paul Erdős (and Rényi may have been thinking of Erdős),...

to prove that the permanent of a matrix with entries from {0,1} has a polynomial-time approximation scheme. In the proof, Jerrum and Sinclair studied the...

clique problem; it may be solved in quasi-polynomial time but is conjectured not to be solvable in polynomial time for intermediate values of the clique...

classification and model selection. Marton was also responsible for the polynomial Freiman–Ruzsa conjecture, a central question of additive combinatorics...

all relevant dates. Alternatively polynomial interpolation or spline interpolation is used where piecewise polynomial functions are fitted in time intervals...

further conjectured that there exists a nonconstant integer-coefficient polynomial whose values at the natural numbers form a Sidon sequence. Specifically...

generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz...

numbers Stirling numbers of the second kind Stirling polynomials Random permutation statistics Rényi, Alfred (1962). "Théorie des éléments saillants d'une...

of nodes. In scale-free networks the degree of the largest hub rises polynomially with the size of the network. Therefore, the degree of a hub can be high...

the chromatic polynomial of the graph, and the chromatic polynomial of the whole graph can be obtained as the product of the polynomials of its components...

{\displaystyle H} -free graphs necessarily contain a perfect induced subgraph of polynomial size. This is because every perfect graph necessarily has either a clique...

famous example of this is Shor's algorithm that can factor numbers in polynomial time, compared to the best classical algorithms that take sub-exponential...