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Hypergraph girth and graph blocks
Connect Berge girth and incidence forests with block decomposition and vertex deletion, supplying induced graph realisations, forbidden-block control and the induction remainder.
1 · Prerequisites
- Finite maximal extension of a 2-connected subgraph
- Every edge belongs to exactly one nontrivial block
- Cutvertices, 2-connected pieces and nontrivial blocks
- Cycles, trees and forests in a simple graph on an arbitrary vertex set
- Subgraphs, induced subgraphs and spanning subgraphs
- A bipartite graph and a proper two-colouring of its vertices
- Reinhard Diestel, Graph Theory, sixth edition, Chapter 3 · Section 3.1, printed p. 64 block definition/overlap paragraph; p. 65 block graph definition; p. 66 Lemma 3.1.4
- A nonempty simple graph is a tree if and only if each pair of vertices is joined by exactly one path
2 · Logical flowchart
Arrows show item dependencies. A grouped prerequisite node points to items that use one or more of its members; their exact links are listed above.
3 · Items
Theorem
Block incidence tree and containment contract
Lemma