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A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

A domatic partition is a partition of the vertices of a graph into disjoint dominating sets. The maximum number of disjoint dominating sets in a domatic partition of a graph ...

An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are ...

The path covering number (or path-covering number; Slater 1972) of a graph G, variously denoted as summarized below, is the minimum number of vertex-disjoint paths that cover ...

A tree (also called a bicentral tree) having two nodes that are graph centers. The numbers of bicentered trees on n=1, 2, ... nodes are 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108 ...

The cycle double cover conjecture states that every bridgeless graph has a collection of cycles which together contain every edge exactly twice. This conjecture remains open, ...

The detour matrix Delta, sometimes also called the maximum path matrix or maximal topological distances matrix, of a graph is a symmetric matrix whose (i,j)th entry is the ...

The maximum possible weight of a fractional clique of a graph G is called the fractional clique number of G, denoted omega^*(G) (Godsil and Royle 2001, pp. 136-137) or ...

The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...

The Robertson-Seymour theorem, also called the graph minor theorem, is a generalization of the Kuratowski reduction theorem by Robertson and Seymour, which states that the ...