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### A generalization of outerplanar graphs

L. Oubiña, R. Zucchello
1984 Discrete Mathematics
l[Rt G be a planar graph and W a set of vertices, G is W-outerplanar if it can be embedded in the plane so that all vertices of W lie on the exterior face.  ...  We give a characterization of these graphs by forbidden subgraphs, an upper bound on the number of edges, and other properties which lead to an algorithm of W-outerplanarity testing.  ...  Fig. 1 . 1 Fig. 1. . , Bk} of V(H), if for every i there is no edge ill H joining two vertices of Bi. Applying Lemma 3.1 it is easy to prove: Lemma 3.2. Let G be a &colorable graph.  ...

### Approximation of pathwidth of outerplanar graphs

Hans L. Bodlaender, Fedor V. Fomin
2002 Journal of Algorithms
In this paper, we give an algorithm, that given a biconnected outerplanar graph G, finds a path decomposition of G of pathwidth at most at most twice the pathwidth of G plus one.  ...  To obtain the result, several relations between the pathwidth of a biconnected outerplanar graph and its dual are established.  ...  Now pw(H * ) ≤ pw(H − ) + 1 ≤ 2 · pw(T ) + 2 = 2 · pw(H) An approximation algorithm for biconnected outerplanar graphs In this section, we give an algorithm, that given a 2-connected outerplanar graph  ...

### Characterizations of outerplanar graphs

Maciej M. Sysło
1979 Discrete Mathematics
Finally, we attempt to generalize these results for k-outerplanar graphs. MTOdUCtiOll The main purpose of this paper is to provide some further characterizations of outerplanar graphs.  ...  The paper presents several characterizations of outerp:anar graphs, some of them are counterparts of the well-known characterizations of planar graphs and the other provide very efficient tools for outerplanarity  ...  If a biconnected graph G is outerplanar then the boundary of the exterior face of its outerplanar embedding is a Hamiltonian cycle, say (v,, 02, q3, l l l 9 v,, v,).  ...

### Approximation of Pathwidth of Outerplanar Graphs [chapter]

Fedor V. Fomin, Hans L. Bodlaender
2001 Lecture Notes in Computer Science
In this paper, we give an algorithm, that given a biconnected outerplanar graph G, finds a path decomposition of G of pathwidth at most at most twice the pathwidth of G plus one.  ...  To obtain the result, several relations between the pathwidth of a biconnected outerplanar graph and its dual are established.  ...  Now pw(H * ) ≤ pw(H − ) + 1 ≤ 2 · pw(T ) + 2 = 2 · pw(H) An approximation algorithm for biconnected outerplanar graphs In this section, we give an algorithm, that given a 2-connected outerplanar graph  ...

### Adjacency posets of outerplanar graphs [article]

Marcin Witkowski
2021 arXiv   pre-print
Felsner, Li and Trotter showed that the dimension of the adjacency poset of an outerplanar graph is at most 5, and gave an example of an outerplanar graph whose adjacency poset has dimension 4.  ...  Add an apex v to an outerplanar graph H with dim(A H ) = 4. The dimension of the subposet defined on H is 4.  ...  When it comes to outerplanar graphs, we know that dimension of incidence poset of the outerplanar graph with no vertices of degree 1 is at most [2 3] .  ...

### Large Induced Acyclic and Outerplanar Subgraphs of 2-Outerplanar Graph

Glencora Borradaile, Hung Le, Melissa Sherman-Bennett
2017 Graphs and Combinatorics
We also show that every 2-outerplanar graph has an induced outerplanar graph on at least two-thirds of its vertices.  ...  We show tighter results for 2-outerplanar graphs.  ...  We thank anonymous reviewers for comments that help improving the presentation of this paper.  ...

### Outerplanar Partitions of Planar Graphs

Kiran S. Kedlaya
1996 Journal of combinatorial theory. Series B (Print)
An outerplanar graph is one that can be embedded in the plane so that all of the vertices lie on one of the faces.  ...  We give a method that yields outerplanar partitions of certain graphs not covered by previous results.  ...  Grant DMS-9225045 and National Security Agency Grant MDA 904-91-H-0036.  ...

### Outerplanarity of line graphs and iterated line graphs

Huiqiu Lin, Weihua Yang, Hailiang Zhang, Jinlong Shu
2011 Applied Mathematics Letters
The outerplanar index of a graph G is the smallest integer k such that the kth iterated line graph of G is non-outerplanar.  ...  In this note, we show: (i) the characterization of the forbidden subgraphs for graphs with outerplanar line graphs; (ii) that the outerplanar index of a graph is either infinite or at most 3.  ...  Acknowledgements The authors are indebted to anonymous referee who spotted a few inaccuracies in the first version of this work and whose suggestions led to considerable improvements in the presentation  ...

### Reconstruction of maximal outerplanar graphs

Bennet Manvel
1972 Discrete Mathematics
We dcai only with MOP graphs containing .H lenst three points, whiich are triangulations of palygons.  ...  An c outerplanar graph is ~~~xinfrtl ou~e~plancrr ('MOP) if no line can be added kthout Iasing oulerplan;rrity.  ...  C: Fig. 1 . Deletion of a point adjacent to a typ@ two point. g3..  ...

### Spanning tree congestion of k-outerplanar graphs

Hans L. Bodlaender, Kyohei Kozawa, Takayoshi Matsushima, Yota Otachi
2011 Discrete Mathematics
We show that his conjecture is true and the bound is tight for outerplanar graphs and k-outerplanar graphs of maximum degree 4.  ...  We give a precise characterization of the spanning tree congestion of outerplanar graphs, and thus show that the spanning tree congestion of outerplanar graphs can be determined in linear time.  ...  On the other hand, any spanning tree of H d has only one u-v path. This implies stc(H d ) ≥ d  . u v u v u v u v H 5 H 7 H 9 H 3 Figure 1: Graphs H d for d ∈ {3, 5, 7, 9}.  ...

### Area-Efficient Drawings of Outerplanar Graphs [chapter]

2004 Lecture Notes in Computer Science
We show that an outerplanar graph G with n vertices and degree d admits a planar straight-line grid drawing with area O(dn 1.48 ) in O(n) time.  ...  For example, in Since f = O(n), h(n) = h (f ) = O(df 0.48 ) = O(dn 0.48 ).Theorem 1. Let G be an outerplanar graph with degree d and n vertices.  ...  Throughout the rest of this paper, for simplicity, by the term outerplanar graph, we will mean a maximal outerplanar graph.  ...

### Planar linear arrangements of outerplanar graphs

G.N. Frederickson, S.E. Hambrusch
1988 IEEE Transactions on Circuits and Systems
Given an n -vertex outerplanar graph G I we consider the problem of arranging the vertices of G on a line such that no two edges cross and various cost measures are minimized.  ...  We present efficient algorithms for generating layouts in which every edge (i ,j) of G does not exceed a given bandwidth b (i ,n, the total edge length and the cutwidth of the layout is minimized. respectively  ...  The graphs that can be laid out under this assumption are exactly the outerplanar graphs [Y2] .  ...

### On packing chromatic number of subcubic outerplanar graphs [article]

Nicolas Gastineau
2018 arXiv   pre-print
We provide asymptotic bounds depending on structural properties of the outerplanar graphs and determine sharper bounds for some classes of subcubic outerplanar graphs.  ...  These subclasses include subcubic trees, base-3 Sierpiński graphs and hexagonal lattices.In this paper we are interested in the packing chromatic number of subcubic outerplanar graphs.  ...  Acknowledgments The authors thank the referees for their judicious comments and Mahmoud Omidvar for his precious help, in particular for providing Pattern (1) of proof of Theorem 3.  ...

### Injective chromatic number of outerplanar graphs [article]

Mahsa Mozafari-Nia, Behnaz Omoomi
2017 arXiv   pre-print
Then, it is proved that for outerplanar graphs with Δ=3, χ_i(G)≤Δ+1 and the bound is tight for outerplanar graphs of girth three and 4.  ...  In this paper, the injective chromatic number of outerplanar graphs with maximum degree Δ and girth g is studied. It is shown that for every outerplanar graph, χ_i(G)≤Δ+2, and this bound is tight.  ...  = c(v j ) = c(v j+1 ) and change the color of v j−1 Theorem 4 . 4  Let G be a connected graph and L be a list-assignment to the vertices,where |L(v)| ≥ deg(v) for each v ∈ V (G).  ...

### On the colorings of outerplanar graphs

Weifan Wang
1995 Discrete Mathematics
In this paper, we have studied seven colorings of outerplanar graphs.  ...  Two main conclusions have been proved: if G is an outerplanar graph without cut vertex and A(G)>/6, then (i) Xef(G) = A(G), and (ii) Zvef(G) = A(G) + 1, where gef and Xva are the edge-face chromatic number  ...  Zhang Zhongfu of Lanzhou Railway Institute of China for his valuable suggestions.  ...
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