2-core of a graph
= 2-core of a graph
{title2=$C_2(G)$}
= Graph 2-core
{synonym}
= 2-core
{synonym}
The 2-core is the unique largest induced <subgraph> with <minimum degree> at least two. It is obtained by repeatedly deleting vertices of degree zero or one. Every subgraph with <minimum degree> two survives each deletion, which proves maximality and order independence. In a connected graph with a nonempty 2-core, the deleted vertices form rooted trees attached individually to the core vertices.