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...

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...

face 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 outerplanar graph is a graph that...

In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k {\displaystyle k} . That...

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...

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...

theorem states that K 4 {\displaystyle K_{4}} and K 2 , 3 {\displaystyle K_{2,3}} are the forbidden minors for the set of outerplanar graphs. Although the Robertson–Seymour...

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

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...

k {\displaystyle k} -outerplanar graph. Many NP-complete problems can be solved with dynamic programming on k {\displaystyle k} -outerplanar graphs....

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

and the maximal outerplanar graphs. The split graphs are exactly the graphs that are chordal and have a chordal complement. The k-trees, central to...

_{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...

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...

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

for graphs of treewidth at most three, for k-connected graphs of treewidth k, for graphs of constant treewidth and chordality, and for k-outerplanar graphs...

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...

problems. The class of GSP-graphs include the classes of SP-graphs and outerplanar graphs. GSP graphs may be specified by Definition 2 augmented with the third...

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

series–parallel graphs, and include also the maximal outerplanar graphs. Planar 3-trees are also known as Apollonian networks. The graphs that have treewidth...

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...

pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian networks. For instance, the series–parallel graphs are a subfamily of the...

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...

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...

Halin graphs and outerplanar graphs", Discrete Mathematics, 256 (1–2): 397–405, doi:10.1016/S0012-365X(01)00302-8, MR 1927561. Shiu, W. C.; Sun, P. K. (2008)...

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...

well-known: the graphs with μ ≤ 1 are the linear forests (disjoint unions of paths), the graphs with μ ≤ 2 are the outerplanar graphs, and the graphs with μ ≤...