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In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

The Hungarian algorithm finds a maximum independent edge set on a graph. The algorithm starts with any matching M and constructs a tree via a breadth-first search to find an ...

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...

Construction of the angle pi/3=60 degrees produces a 30-60-90 triangle, which has angles theta=pi/3 and theta/2=pi/6. From the above diagram, write y=sintheta for the ...

Construction of the angle pi/6=30 degrees produces a 30-60-90 triangle, which has angles theta=pi/6 and 2theta=pi/3. From the above diagram, write y=sintheta for the vertical ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...