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If A, B, and C are three points on one line, D, E, and F are three points on another line, and AE meets BD at X, AF meets CD at Y, and BF meets CE at Z, then the three points ...

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 ...

The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...