részgráfban

A részgráfban, often translated as "subgraph" in English, refers to a fundamental concept in graph theory. A subgraph of a graph G is a graph H that can be formed by selecting a subset of the vertices of G and a subset of the edges of G. Crucially, the edges in H must connect only vertices that are also present in H.

There are different types of subgraphs. An induced subgraph is created by selecting a subset of vertices and including *all* edges from the original graph that connect pairs of those selected vertices. In contrast, a general subgraph allows for the selection of both vertices and edges, where the edges do not necessarily have to connect all pairs of selected vertices.

The concept of subgraphs is essential for analyzing the structure and properties of larger graphs. By examining subgraphs, mathematicians and computer scientists can identify patterns, solve complex problems, and understand the relationships within a network. For instance, finding specific types of subgraphs, such as cliques or cycles, can reveal important characteristics of the graph's connectivity or underlying processes. The study of subgraphs is a cornerstone of graph theory with applications in diverse fields like computer science, social network analysis, and molecular biology.