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A generalization of outerplanar graphs

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

2002
*
Journal of Algorithms
*

In this paper, we give an algorithm, that given a biconnected

doi:10.1016/s0196-6774(02)00001-9
fatcat:prnxgwidyfaspiiybzwoayzh2i
*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

1979
*
Discrete Mathematics
*

Finally, we attempt to generalize these results for k-

doi:10.1016/0012-365x(79)90060-8
fatcat:2wb7tontlbeqrkea4mdjpca5um
*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]

2001
*
Lecture Notes in Computer Science
*

In this paper, we give an algorithm, that given a biconnected

doi:10.1007/3-540-45477-2_16
fatcat:xeri43chz5bzdomulyi6wkytdy
*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]

2021
*
arXiv
*
pre-print

Felsner, Li and Trotter showed that the dimension

arXiv:2001.09497v3
fatcat:3hf3sqhvkvgslp36d6gic2o4re
*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

2017
*
Graphs and Combinatorics
*

We also show that every 2-

doi:10.1007/s00373-017-1859-3
fatcat:k25ps3hsi5ac7mnmlyvvh7kpa4
*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

1996
*
Journal of combinatorial theory. Series B (Print)
*

An

doi:10.1006/jctb.1996.0043
fatcat:m2rilfaia5ctrlcdyecmmm5sn4
*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

2011
*
Applied Mathematics Letters
*

The

doi:10.1016/j.aml.2011.02.011
fatcat:hrjke2llinauzd4yont22ddhtq
*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

1972
*
Discrete Mathematics
*

We dcai only with MOP

doi:10.1016/0012-365x(72)90007-6
fatcat:oqwsr676dnatllhzifgq56qsk4
*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

2011
*
Discrete Mathematics
*

We show that his conjecture is true and the bound is tight for

doi:10.1016/j.disc.2011.03.002
fatcat:5phvbou4ljc5pbfz7drlpw77mm
*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 [14] . 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

doi:10.1007/978-3-540-24595-7_12
fatcat:udtxchzzi5bnji6bozpktj6bey
*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

1988
*
IEEE Transactions on Circuits and Systems
*

Given an n -vertex

doi:10.1109/31.1745
fatcat:nffllelyrbanjcuhkaop4lliom
*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]

2018
*
arXiv
*
pre-print

We provide asymptotic bounds depending on structural properties

arXiv:1703.05023v3
fatcat:zbq4yrxf3ff33geqscf75wwpau
*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]

2017
*
arXiv
*
pre-print

Then, it is proved that for

arXiv:1706.02335v1
fatcat:yqou65d7ofhtloemdiqx4gaxte
*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 [12] 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

1995
*
Discrete Mathematics
*

In this paper, we have studied seven colorings

doi:10.1016/0012-365x(94)00242-b
fatcat:km3hmdmecza6lb5eeoh3tcr4ia
*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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