In graph theory, a cactus (sometimes called a cactus tree) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently...

Block graphs are sometimes erroneously called Husimi trees (after Kôdi Husimi), but that name more properly refers to cactus graphs, graphs in which...

in the graph shares at most one vertex. The family of graphs in which each connected component is a cactus graph is downwardly closed under graph minor...

distance graphs include the cactus graphs, the matchstick graphs and penny graphs, and the hypercube graphs. The generalized Petersen graphs are non-strict...

graphs. The Cactus graph is a graph-based structure specifically designed for whole-genome multiple alignments with complex rearrangements. A cactus graph...

graph F2 is isomorphic to the butterfly graph. Friendship graphs are generalized by the triangular cactus graphs. The friendship theorem of Paul Erdős,...

Examples of locally linear graphs include the triangular cactus graphs, the line graphs of 3-regular triangle-free graphs, and the Cartesian products...

In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

These include: Bipartite graph, a graph without odd cycles (cycles with an odd number of vertices) Cactus graph, a graph in which every nontrivial biconnected...

Cactus, alternative name of the Mammillaria cactus genera Cactus (crustacean), the crustacean genus Cactus graph or cactus, a type of connected graph...

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

algorithms exist for cographs, chain graphs, and cactus block graphs (a class including both cactus graphs and block graphs). The problem may be solved in polynomial...

a cycle graph is geodetic when it has odd length, every cactus graph in which the cycles have odd length is also geodetic. These cactus graphs are exactly...

butterfly, the resulting larger graph family consists of the cactus graphs and disjoint unions of multiple cactus graphs. More simply, if multigraphs with...

of graphs, including series–parallel graphs and their subgraphs, which include outerplanar graphs, as well as for a line graph of a tree or a cactus graph...

components as the original graph. Cactus graphs are automatically planar graphs, and the problem of finding triangular cactus graphs forms the basis for the...

path graphs), pseudoforests, and cactus graphs; planar graphs, outerplanar graphs, apex graphs (formed by adding a single vertex to a planar graph), toroidal...

mathematical area of graph theory, the name "Husimi tree" has come to refer to two different kinds of graphs: cactus graphs (the graphs in which each edge...

bipartite graphs, all cactus graphs, all wheel graphs, all graphs on at most six vertices, and almost every k {\displaystyle k} -colorable graph. Although...

k, the graphs of treewidth at most k are called the partial k-trees. Other families of graphs with bounded treewidth include the cactus graphs, pseudoforests...

Families of graphs with this property include the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian...

conjecture is called a cycle double cover. Some graphs such as cycle graphs and bridgeless cactus graphs can only be covered by using the same cycle more...

other; in this case, it may be represented as the graphic matroid of a cactus graph. If M {\displaystyle M} is a binary matroid, then so is its dual, and...

forests with maximum degree 3. Cactuses: χ g ( C ) = 5 {\displaystyle \chi _{g}({\mathcal {C}})=5} . Outerplanar graphs: 6 ≤ χ g ( O ) ≤ 7 {\displaystyle...

exploiting the properties of cactus graphs, Leighton & Moitra (2010) proved the conjecture; the greedy embeddings of these graphs can be defined succinctly...

problem global optimum gnome sort goobi graph graph coloring graph concentration graph drawing graph isomorphism graph partition Gray code greatest common...

to: Domesticated hedgehog Hedgehog (band), a Beijing rock band Hedgehog cactus (disambiguation), a common name for Pediocactus, Echinocereus, or Echinopsis...

Graphs are unavailable due to technical issues. Updates on reimplementing the Graph extension, which will be known as the Chart extension, can be found...

numerical grids used for graph plotting or computational simulation, and would be better suited if specific areas of graphs which needed precision could...