Other Properties
Outerplanar graphs have degeneracy at most two: every subgraph of an outerplanar graph contains a vertex with degree at most two.
Outerplanar graphs have treewidth at most two, which implies that many graph optimization problems that are NP-complete for arbitrary graphs may be solved in polynomial time by dynamic programming when the input is outerplanar. More generally, k-outerplanar graphs have treewidth O(k).
Every outerplanar graph can be represented as an intersection graph of axis-aligned rectangles in the plane, so outerplanar graphs have boxicity at most two.
A graph is outerplanar if and only if its Colin de Verdière graph invariant is at most two. The graphs characterized in a similar way by having Colin de Verdière invariant at most one, three, or four are respectively the linear forests, planar graphs, and linklessly embeddable graphs.
Read more about this topic: Outerplanar Graph
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