részgráfot

A részgráfot, often translated as subgraph, is a fundamental concept in graph theory. A graph is defined by a set of vertices (nodes) and a set of edges connecting pairs of these vertices. A subgraph is essentially a smaller graph that is contained within a larger graph.

Formally, let G = (V, E) be a graph, where V is the set of vertices and E is the set of edges. A subgraph H of G, denoted by H ⊆ G, is a graph H = (V', E') where V' is a subset of V (V' ⊆ V) and E' is a subset of E (E' ⊆ E). Additionally, for every edge e in E', both of its incident vertices must also be present in V'. In simpler terms, a subgraph consists of some (or all) of the vertices of the original graph and some (or all) of the edges of the original graph, with the constraint that no edge is included if its endpoints are not in the selected subset of vertices.

There are different types of subgraphs. A spanning subgraph is a subgraph that contains all the vertices of the original graph. A induced subgraph is formed by selecting a subset of vertices and including all the edges from the original graph that connect pairs of these selected vertices. Other types include paths, cycles, and trees, which can all be considered specific forms of subgraphs. The study of subgraphs is crucial for understanding the structure and properties of larger graphs, and it finds applications in various fields like computer science, network analysis, and operations research.