A maximal outerplanar graph and its 3-coloringThe complete graph K4 is the smallest planar graph that is not outerplanar.
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 graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors K4 and K2,3, or by their Colin de Verdière graph invariants.
They have Hamiltonian cycles if and only if they are biconnected, in which case the outer face forms the unique Hamiltonian cycle. Every outerplanar graph is 3-colorable, and has degeneracy and treewidth at most 2.
The outerplanar graphs are a subset of the planar graphs, the subgraphs of series–parallel graphs, and the circle graphs. The maximal outerplanar graphs, those to which no more edges can be added while preserving outerplanarity, are also chordal graphs and visibility graphs.
graph theory, an outerplanargraph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar graphs...
results in a (k – 1)-outerplanar embedding. A graph is k-outerplanar if it has a k-outerplanar embedding. A Halin graph is a graph formed from an undirected...
Oriented graph, used by some authors as a synonym for a directed graph. out-degree See degree. outer See face. outerplanar An outerplanargraph is a graph that...
as a minor; an outerplanargraph cannot contain K3,2 as a minor (These are not sufficient conditions for planarity and outerplanarity, but necessary)...
maximal outerplanargraph is a graph formed by a simple polygon in the plane by triangulating its interior. Every maximal outerplanargraph is pancyclic...
cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanargraphs. Over time, a number of algorithms...
graph. Every outerplanargraph is also a circle graph. The circle graphs are generalized by the polygon-circle graphs, intersection graphs of polygons...
forests, the interval graphs, and the maximal outerplanargraphs. The split graphs are exactly the graphs that are chordal and have a chordal complement...
graphs are (3,6)-sparse. However, not every (3,6)-sparse graph is planar. Similarly, outerplanargraphs are (2,3)-sparse and planar bipartite graphs are...
for certain cubic graphs such as cubic Hamiltonian graphs. He showed that in case of outerplanargraph of maximum degree 4, the incidence chromatic number...
cut-vertex) is an edge or a cycle. Cacti are outerplanargraphs. Every pseudotree is a cactus. A nontrivial graph is a cactus if and only if every block is...
complete graphs. The graphs with book thickness one are the outerplanargraphs. The graphs with book thickness at most two are the subhamiltonian graphs, which...
is a connected bipartite graph and G ∈ N, then W(G) ≤ diam(G) (∆(G) − 1) + 1. Interval edge-colorings of outerplanargraphs were investigated by Giaro...
planar graphs, or equivalently planar 3-trees. Maximal outerplanargraphs are a subclass of 2-trees, and therefore are also chordal. Chordal graphs are a...
subgraph of an outerplanargraph is outerplanar and every graph obtained by contracting edges of an outerplanargraph is outerplanar. This implies that...
plane graph is the subgraph of the dual graph whose vertices correspond to the bounded faces of the primal graph. A plane graph is outerplanar if and...
complete graph. Trees Disconnected graphs Unit interval graphs Separable graphs without end vertices Maximal planar graphs Maximal outerplanargraphs Outerplanar...
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...
graph is always subhamiltonian. Heath, Lenwood S. (1987), "Embedding outerplanargraphs in small books", SIAM Journal on Algebraic and Discrete Methods, 8...
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