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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 matrix tree theorem, also called Kirchhoff's matrix-tree theorem (Buekenhout and Parker 1998), states that the number of nonidentical spanning trees of a graph G is equal ...

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 ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...