Graph invariants | Spanning tree

Arboricity

The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of spanning forests needed to cover all the edges of the graph. The Nash-Williams theorem provides necessary and sufficient conditions for when a graph is k-arboric. (Wikipedia).

Arboricity
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Related pages

Graphs and Combinatorics | Nash-Williams theorem | Goldberg–Seymour conjecture | Linear arboricity | Planar graph | Discrete Mathematics (journal) | Pseudoforest | Slope number | Degree (graph theory) | Tree (graph theory) | Complete bipartite graph | Induced subgraph | Strength of a graph | Graph partition | Fáry's theorem | Matroid partitioning | Journal of Combinatorial Theory | Linear forest | Degeneracy (graph theory) | Star (graph theory) | Dense graph | Thickness (graph theory)