Search Results for ""

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

Let a sequence be defined by A_(-1) = s (1) A_0 = 3 (2) A_1 = r (3) A_n = rA_(n-1)-sA_(n-2)+A_(n-3). (4) Also define the associated polynomial f(x)=x^3-rx^2+sx+1, (5) and let ...

For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

Let L be a lattice (or a bounded lattice or a complemented lattice, etc.), and let C_L be the covering relation of L: C_L={(x,y) in L^2|x covers y or y covers x}. Then C_L is ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

The reflexive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same reflexive closure as R. Thus aR^'b for any elements a and b of X, ...

A set S together with a relation >= which is both transitive and reflexive such that for any two elements a,b in S, there exists another element c in S with c>=a and c>=b. In ...