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Let (A,<=) and (B,<=) be totally ordered sets. Let C=A×B be the Cartesian product and define order as follows. For any a_1,a_2 in A and b_1,b_2 in B, 1. If a_1<a_2, then ...

An urelement contains no elements, belongs to some set, and is not identical with the empty set (Moore 1982, p. 3; Rubin 1967, p. 23). "Ur" is a German prefix which is ...

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

A bicubic graph is a bipartite cubic graph. Tutte (1971) conjectured that all 3-connected bicubic graphs are Hamiltonian (the Tutte conjecture), but a number of bicubic ...

A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...

The Sierpiński gasket graph of order n is the graph obtained from the connectivity of the Sierpiński sieve. The first few Sierpiński gasket graphs are illustrated above. S_2 ...

Any tangle obtained by additions and multiplications of rational tangles (Adams 1994).

One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of a set x such that, for any y of a, if there exists a z satisfying A(y,z), then such z exists ...

One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as exists x forall y(!y in x).

A matching is a maximum matching iff it contains no augmenting path.