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On the Orthogonal Drawing of Outerplanar Graphs [PDF]
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2004 In this paper we show that an outerplanar graph G with maximum degree at most 3 has a 2-D orthogonal drawing with no bends if and only if G contains no triangles. We also show that an outerplanar graph G with maximum degree at most 6 has a 3-D orthogonal drawing with no bends if and only if G contains no triangles.
Kumiko Nomura +2 more
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Journal of Algorithms, 1996
Summary: We show that for outerplanar graphs \(G\) the problem of augmenting \(G\) by adding a minimum number of edges such that the augmented graph \(G'\) is planar and bridge-connected, biconnected, or triconnected can be solved in linear time and space.
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Summary: We show that for outerplanar graphs \(G\) the problem of augmenting \(G\) by adding a minimum number of edges such that the augmented graph \(G'\) is planar and bridge-connected, biconnected, or triconnected can be solved in linear time and space.
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An algorithm for outerplanar graphs with parameter
Journal of Algorithms, 1991Summary: For \(n\)-vertex outerplanar graphs, it is proven that \(O(n^{2.87})\) is an upper bound on the number of breakpoints of the function which gives the maximum weight of an independent set, where the vertex weights vary as linear functions of a parameter. An \(O(n^{2.87})\) algorithm for finding the solution is proposed.
Binghuan Zhu, Wayne Goddard
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A characterization of ?-outerplanar graphs
Journal of Graph Theory, 1996The graphs investigated in this paper can have loops and parallel edges. An outerplanar graph is a graph that has a planar embedding in which all its vertices lie on the boundary of the infinite face. And an \(\alpha\)-outerplanar graph is a graph \(G\) which is not outerplanar such that, for some edge \(\alpha\), both the deletion \(G\backslash \alpha\
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Centers of maximal outerplanar graphs
Journal of Graph Theory, 1980AbstractThe center of a graph is defined to be the subgraph induced by the set of vertices that have minimum eccentricities (i.e., minimum distance to the most distant vertices). It is shown that only seven graphs can be centers of maximal outerplanar graphs.
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Independent covers in outerplanar graphs
1988A subset U of vertices of a plane graph is said to be a perfect face-independent vertex cover (FIVC) if and only if each face has exactly one vertex in U. Necessary and sufficient conditions for a maximal plane graph to have a perfect FIVC are derived.
Maciej M. Sysło, Pawel Winter
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Linear algorithms to recognize outerplanar and maximal outerplanar graphs
Information Processing Letters, 1979openaire +2 more sources