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When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

The vertex connectivity kappa(G) of a graph G, also called "point connectivity" or simply "connectivity," is the minimum size of a vertex cut, i.e., a vertex subset S subset= ...

A local sink is a node of a directed graph with no exiting edges, also called a terminal (Borowski and Borwein 1991, p. 401; left figure). A global sink (often simply called ...

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 ...

For |z|<1, product_(k=1)^infty(1+z^k)=product_(k=1)^infty(1-z^(2k-1))^(-1). (1) Both of these have closed form representation 1/2(-1;z)_infty, (2) where (a;q)_infty is a ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...