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A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

The Petersen graph is the cubic graph on 10 vertices and 15 edges which is the unique (3,5)-cage graph (Harary 1994, p. 175), as well as the unique (3,5)-Moore graph. It can ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

The Erdős number is the number of "hops" needed to connect the author of a paper with the prolific late mathematician Paul Erdős. An author's Erdős number is 1 if he has ...

Due to Lebesgue and Brouwer. If an n-dimensional figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least n+1 of ...

A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...

A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of ...

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

The Weierstrass substitution is the trigonometric substitution t=tan(theta/2) which transforms an integral of the form intf(costheta,sintheta)dtheta into one of the form ...