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A forest is an acyclic graph (i.e., a graph without any graph cycles). Forests therefore consist only of (possibly disconnected) trees, hence the name "forest." Examples of ...

A partition {a_1,...,a_n} is called graphical if there exists a graph G having degree sequence {a_1,...,a_n}. The number of graphical partitions of length n is equal to the ...

A number n for which the harmonic mean of the divisors of n, i.e., nd(n)/sigma(n), is an integer, where d(n)=sigma_0(n) is the number of positive integer divisors of n and ...

A word is said to be overlapfree if it has no subwords of the form xyxyx. A squarefree word is overlapfree, and an overlapfree word is cubefree. The numbers t(n) of binary ...

The sequence of Fibonacci numbers {F_n} is periodic modulo any modulus m (Wall 1960), and the period (mod m) is the known as the Pisano period pi(m) (Wrench 1969). For m=1, ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...

A number (usually base 10 unless specified otherwise) which has no digitaddition generator. Such numbers were originally called Colombian numbers (S. 1974). There are ...

The most common statement known as Steiner's theorem (Casey 1893, p. 329) states that the Pascal lines of the hexagons 123456, 143652, and 163254 formed by interchanging the ...