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There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...

Seymour conjectured that a graph G of order n with minimum vertex degree delta(G)>=kn/(k+1) contains the kth graph power of a Hamiltonian cycle, generalizing Pósa's ...

Twenty golfers wish to play in foursomes for 5 days. Is it possible for each golfer to play no more than once with any other golfer? The answer is yes, and the following ...

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

A method of solving combinatorial problems by means of an algorithm which is allowed to run forward until a dead end is reached, at which point previous steps are retraced ...

An origami configuration that can be pressed to a plane figure without crumpling it or adding new creases.

Let p and q be partitions of a positive integer, then there exists a (0,1)-matrix A such that c(A)=p, r(A)=q iff q is dominated by p^*.

Hackenbush is a game in combinatorial game theory in which player Left can delete any bLue edge, player Right can delete any Red edge, and either player can delete Green ...

The matrix tree theorem, also called Kirchhoff's matrix-tree theorem (Buekenhout and Parker 1998), states that the number of nonidentical spanning trees of a graph G is equal ...