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The graph complement of a graph hole. Graph antiholes are called even if they have an even number of vertices and odd if they have an odd number of vertices (Chvátal). No odd ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as ...

Let c_k be the number of edge covers of a graph G of size k. Then the edge cover polynomial E_G(x) is defined by E_G(x)=sum_(k=0)^mc_kx^k, (1) where m is the edge count of G ...

Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

A stacked (or generalized) prism graph Y_(m,n) is a simple graph given by the graph Cartesian product Y_(m,n)=C_m square P_n (Gallian 2007) for positive integers m,n with ...

A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect. ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

Seymour conjectured that a graph G of order n with minimum vertex degree delta(G)>=kn/(k+1) contains the kth graph power of a Hamiltonian cycle, generalizing Pósa's ...