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The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled ...

Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

The rhombic triacontahedral graph is Archimedean dual graph which is the skeleton of the rhombic triacontahedron, great rhombic triacontahedron, and small triambic ...