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Every graph with n vertices and maximum vertex degree Delta(G)<=k is (k+1)-colorable with all color classes of size |_n/(k+1)_| or [n/(k+1)], where |_x_| is the floor ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

An alternating sign matrix is a matrix of 0s, 1s, and -1s in which the entries in each row or column sum to 1 and the nonzero entries in each row and column alternate in ...

Every "large" even number may be written as 2n=p+m where p is a prime and m in P union P_2 is the set of primes P and semiprimes P_2.

A plane partition whose solid Ferrers diagram is invariant under the rotation which cyclically permutes the x-, y-, and z-axes. Macdonald's plane partition conjecture gives a ...

Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v ...

The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

The middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...