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...

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...

In graph theory, a k-outerplanar graph is a planar graph that has a planar embedding in which the vertices belong to at most k {\displaystyle k} concentric...

  Oriented graph, used by some authors as a synonym for a directed graph. out-degree See degree. outer See face. outerplanar An outerplanar graph is a graph that...

as a minor; an outerplanar graph cannot contain K3,2 as a minor (These are not sufficient conditions for planarity and outerplanarity, but necessary)...

polyhedron Outerplanar graph Random graph Regular graph Scale-free network Snark (graph theory) Sparse graph Sparse graph code Split graph String graph Strongly...

any Turán graph is locally Turán. Every planar graph is locally outerplanar. However, not every locally outerplanar graph is planar. A graph is triangle-free...

maximal outerplanar graph is a graph formed by a simple polygon in the plane by triangulating its interior. Every maximal outerplanar graph is pancyclic...

complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are the subhamiltonian graphs, which...

5-degenerate, and the degeneracy of any planar graph is at most five. Similarly, every outerplanar graph has degeneracy at most two, and the Apollonian...

for certain cubic graphs such as cubic Hamiltonian graphs. He showed that in case of outerplanar graph of maximum degree 4, the incidence chromatic number...

graphs are (3,6)-sparse. However, not every (3,6)-sparse graph is planar. Similarly, outerplanar graphs are (2,3)-sparse and planar bipartite graphs are...

forests, the interval graphs, and the maximal outerplanar graphs. The split graphs are exactly the graphs that are chordal and have a chordal complement...

cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs. Over time, a number of algorithms...

subgraph of an outerplanar graph is outerplanar and every graph obtained by contracting edges of an outerplanar graph 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...

graph. Every outerplanar graph is also a circle graph. The circle graphs are generalized by the polygon-circle graphs, intersection graphs of polygons...

is a connected bipartite graph and G ∈ N, then W(G) ≤ diam(G) (∆(G) − 1) + 1. Interval edge-colorings of outerplanar graphs were investigated by Giaro...

Nonetheless, every outerplanar graph of maximum degree d has an outerplanar drawing with angular resolution proportional to 1/d. For planar graphs with maximum...

cut-vertex) is an edge or a cycle. Cacti are outerplanar graphs. Every pseudotree is a cactus. A nontrivial graph is a cactus if and only if every block is...

near-linear area, depending on the drawing style. Every outerplanar graph has a straight-line outerplanar drawing with area subquadratic in its number of vertices...

for outerplanar graphs. The same authors proved that n ≤ ( D β + 1 ) t − 1 {\displaystyle n\leq (D\beta +1)^{t-1}} for graphs with no complete graph of...

planar graphs, or equivalently planar 3-trees. Maximal outerplanar graphs are a subclass of 2-trees, and therefore are also chordal. Chordal graphs are a...

1-planar graph. The class of graphs analogous to outerplanar graphs for 1-planarity are called the outer-1-planar graphs. These are graphs that can be...

complete graph. Trees Disconnected graphs Unit interval graphs Separable graphs without end vertices Maximal planar graphs Maximal outerplanar graphs Outerplanar...

n-vertex graph is outerplanar, then μ ≥ n − 4; If the complement of an n-vertex graph is planar, then μ ≥ n − 5. A minor of a graph is another graph formed...

_{g}({\mathcal {C}})=5} . Outerplanar graphs: 6 ≤ χ g ( O ) ≤ 7 {\displaystyle 6\leq \chi _{g}({\mathcal {O}})\leq 7} . Planar graphs: 7 ≤ χ g ( P ) ≤ 17 {\displaystyle...

graph is always subhamiltonian. Heath, Lenwood S. (1987), "Embedding outerplanar graphs in small books", SIAM Journal on Algebraic and Discrete Methods, 8...

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...

separates outerplanar graphs from their generalization series–parallel graphs: it may be solved in polynomial time for 2-connected outerplanar graphs, but...