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A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...

The lower independence number i(G) of a graph G is the minimum size of a maximal independent vertex set in G. The lower indepedence number is equiavlent to the "independent ...

Multiple edges are two or more edges connecting the same two vertices within a multigraph. Multiple edges of degree d_(ij) between vertex i and vertex j correspond to an ...

A sequence of positive integers 1<=a_1<a_2<a_3<... (1) is a nonaveraging sequence if it contains no three terms which are in an arithmetic progression, i.e., terms such that ...

The (26,8)-Paulus graph having the largest possible graph automorphism group order of all 26-node Paulus graphs (namely 120) is sometimes known as the ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

Dirac (1952) proved that if the minimum vertex degree delta(G)>=n/2 for a graph G on n>=3 nodes, then G contains a Hamiltonian cycle (Bollobás 1978, Komlós et al. 1996). In ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

The mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. Ramsey theory is named after Frank ...

A random graph is a graph in which properties such as the number of graph vertices, graph edges, and connections between them are determined in some random way. The graphs ...