Block graph

In graph theory, a branch of combinatorial mathematics, a block graph or clique tree^[1] is a type of undirected graph in which every biconnected component (block) is a clique.

Block graphs are sometimes erroneously called Husimi trees (after Kôdi Husimi),^[2] but that name more properly refers to cactus graphs, graphs in which every nontrivial biconnected component is a cycle.^[3]

Block graphs may be characterized as the intersection graphs of the blocks of arbitrary undirected graphs.^[4]

^ Vušković, Kristina (2010), "Even-hole-free graphs: A survey" (PDF), Applicable Analysis and Discrete Mathematics, 4 (2): 219–240, doi:10.2298/AADM100812027V.
^ Cite error: The named reference h79 was invoked but never defined (see the help page).
^ See, e.g., MR0659742, a 1983 review by Robert E. Jamison of another paper referring to block graphs as Husimi trees; Jamison attributes the mistake to an error in a book by Mehdi Behzad and Gary Chartrand.
^ Harary, Frank (1963), "A characterization of block-graphs", Canadian Mathematical Bulletin, 6 (1): 1–6, doi:10.4153/cmb-1963-001-x, hdl:10338.dmlcz/101399.

[v10-1] Vušković, Kristina (2010), "Even-hole-free graphs: A survey" (PDF), Applicable Analysis and Discrete Mathematics, 4 (2): 219–240, doi:10.2298/AADM100812027V.

[h79-2] Cite error: The named reference h79 was invoked but never defined (see the help page).

[3] See, e.g., MR0659742, a 1983 review by Robert E. Jamison of another paper referring to block graphs as Husimi trees; Jamison attributes the mistake to an error in a book by Mehdi Behzad and Gary Chartrand.

[h63-4] Harary, Frank (1963), "A characterization of block-graphs", Canadian Mathematical Bulletin, 6 (1): 1–6, doi:10.4153/cmb-1963-001-x, hdl:10338.dmlcz/101399.

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