Every finite forest has either an isolated vertex (incident to no edges) or a leaf vertex (incident to exactly one edge); therefore, trees and forests are 1-degenerate graphs. Every 1-degenerate graph is a forest. See more

A k-core of a graph G is a maximal connected subgraph of G in which all vertices have degree at least k. Equivalently, it is one of the connected components of … See more

Although concepts of degeneracy and coloring number are frequently considered in the context of finite graphs, the original motivation for Erdős … See more

The coloring number of a graph G was defined by Erdős & Hajnal (1966) to be the least κ for which there exists an ordering of the vertices of G in which each vertex has fewer than κ … See more

If a graph G is oriented acyclically with outdegree k, then its edges may be partitioned into k forests by choosing one forest for each outgoing edge of each node. Thus, the See more

• Graph theory
• Network science
• Percolation Theory
• Core–periphery structure
• Cereceda's conjecture See more