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##
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A linear algorithm for the Hamiltonian completion number of the line graph of a cactus

2001
*
Electronic Notes in Discrete Mathematics
*

Given

doi:10.1016/s1571-0653(05)80070-8
fatcat:djcokupptreghaampyli2ofqni
*a**graph*G = ... SkupieÃ n*for*his personal comments and suggestions on this work and two anonymous referees*for*their helpful comments. ... In this paper,*a**linear**algorithm**for*ÿnding*the**Hamiltonian**completion**number**of**the**line**graph*L(C) (as well as*a*MDTS*of*C)*of**a**cactus*C is proposed. ...##
###
A linear algorithm for the Hamiltonian completion number of the line graph of a cactus

2004
*
Discrete Applied Mathematics
*

Given

doi:10.1016/s0166-218x(03)00441-4
fatcat:po4fekjolfbphjz6uyzjraxwfa
*a**graph*G = ... SkupieÃ n*for*his personal comments and suggestions on this work and two anonymous referees*for*their helpful comments. ... In this paper,*a**linear**algorithm**for*ÿnding*the**Hamiltonian**completion**number**of**the**line**graph*L(C) (as well as*a*MDTS*of*C)*of**a**cactus*C is proposed. ...##
###
Algorithms for Maximum Internal Spanning Tree Problem for Some Graph Classes
[article]

2021
*
arXiv
*
pre-print

In this paper, we propose

arXiv:2112.02248v2
fatcat:sypp5xi27jhs3mfh3cl72g4rxy
*linear*-time*algorithms*to compute*a*maximum internal spanning tree*of*cographs, block*graphs*,*cactus**graphs*, chain*graphs*and bipartite permutation*graphs*. ...*For**a*given*graph*G,*a*maximum internal spanning tree*of*G is*a*spanning tree*of*G with maximum*number**of*internal vertices. ... We also investigated*cactus**graphs*and cographs, finding*linear*-time*algorithms**for**the*MIST problem*for*each*of*these*graph*classes. ...##
###
Page 3646 of Mathematical Reviews Vol. , Issue 89G
[page]

1989
*
Mathematical Reviews
*

*The*min cut

*linear*arrangement problem asks,

*for*

*a*given

*graph*G and positive integer k, whether there exists

*a*

*linear*arrangement

*of*G’s vertices such that any

*line*separating consecutive vertices 05 ... (

*A*

*cactus*is an outerplanar

*graph*such that no two cycles share

*a*common edge.) (4) There is an approximation

*algorithm*that determines

*a*min cut

*linear*arrangement

*of*an outerplanar

*graph*G within

*a*factor ...

##
###
Optimal Hamiltonian completions and path covers for trees, and a reduction to maximum flow

2002
*
ANZIAM journal (Print)
*

*For*arbitrary

*graphs*, constructing

*a*minimum

*Hamiltonian*

*completion*or path cover is clearly NP-hard, but there exists

*a*lineartime

*algorithm*

*for*trees. ...

*A*minimum

*Hamiltonian*

*completion*

*of*

*a*

*graph*G is

*a*minimum-size set

*of*edges that, when added to G, guarantee

*a*

*Hamiltonian*path. ... Several years later, Karejan and Mosesjan [9] gave

*a*polynomial-time

*algorithm*

*for*acyclic digraphs, and Kornienko [10] reported

*a*

*linear*-time

*algorithm*to solve

*the*problem

*for*any

*cactus*,

*a*

*graph*...

##
###
Computing compatible tours for the symmetric traveling salesman problem

2010
*
Mathematical Programming Computation
*

We then describe

doi:10.1007/s12532-010-0021-5
fatcat:x7dryg27ifecpi3hplp2fmkcdm
*a*branch-and-cut*algorithm**for*computing*the*best compatible tour, and present extensive computational results*for*TSPLIB instances. ... We prove that finding*the*best compatible tour is N P-hard and show that*the*tour can have*a*cost approaching 5/3 that*of**the*optimal tour. ... We warmly thank two anonymous referees and*the*editors*for*very useful comments which helped to clarify and improve*the*paper. ...##
###
Vertex and Tree Arboricities of Graphs

2004
*
Journal of combinatorial optimization
*

This paper studies

doi:10.1023/b:joco.0000038912.82046.17
fatcat:zq75b47o3ffjjkd7s2r6r76gde
*the*vertex and*the*tree arboricities on various classes*of**graphs**for*exact values,*algorithms*, bounds, hamiltonicity and NP-*completeness*. ...*The*vertex (respectively, tree) arboricity*of**a**graph*G is*the*minimum*number*va(G) (respectively, ta(G))*of*subsets into which*the*vertices*of*G can be partitioned so that each subset induces*a*forest ... Acknowledgments We thank*the*referees*for*many constructive suggestions. ...##
###
Page 5779 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

*The*total binding

*number*is also given

*for*

*the*path,

*the*cycle,

*the*

*complete*

*graph*and

*the*

*complete*bipartite

*graph*. ... We give

*a*

*linear*(O(|V|+|E|))

*algorithm*to solve this problem on

*a*permutation

*graph*.” ...

##
###
Author index to volume

2004
*
Discrete Applied Mathematics
*

Meloni,

doi:10.1016/s0166-218x(03)00669-3
fatcat:nplxrn6oxbdvpf2t3cyzo7wugu
*A**linear**algorithm**for**the**Hamiltonian**completion**number**of**the**line**graph**of**a**cactus*(2-3) 197-215 Epping, Th., W. Hochst. attler and P. ... Walther, Edge-oblique polyhedral*graphs*(2-3) 315-327 Shamir, R. and R. Sharan,*A*fully dynamic*algorithm**for*modular decomposition and recognition*of*cographs (2-3) 329-340 Sharan, R., see R. ...##
###
Peeling and Nibbling the Cactus: Subexponential-Time Algorithms for Counting Triangulations and Related Problems

2016
*
International Symposium on Computational Geometry
*

Based on

doi:10.4230/lipics.socg.2016.52
dblp:conf/compgeom/MarxM16
fatcat:bdpig53xlfdg3hbri3corqqcim
*the*above*algorithm*, we develop*a*simple and formal framework to count other non-crossing straight-*line**graphs*in n O( √ n) time. ...*The*definition*of**the*separators are based on*the*decomposition*of**the*triangulation into nested layers ("*cactus**graphs*"). ...*For*convenience, we do not require*cactus**graphs*to be connected.*A*triangulation*of**a*set*of*points is*a*maximal plane*graph*on those points. ...##
###
Separating maximally violated comb inequalities in planar graphs
[chapter]

1996
*
Lecture Notes in Computer Science
*

Our

doi:10.1007/3-540-61310-2_35
fatcat:qvegfj6eondkxmvt52tfxaagve
*algorithm*runs in O(n + MC(n)) time, where MC(n) is*the*time to compute all minimum cuts*of**a*planar*graph*. ... Much*of**the*research in this area has been focused on nding new classes*of*facets*for**the*TSP polytope, and much less attention has been paid to*algorithms**for*separating from these classes*of*facets. ... In 7], Gabow gives an O(m + 2 log( n ))*algorithm*to construct*a**cactus*tree in unweighted*graphs*. We are interested in*the**cactus*tree representation*of**a*weighted*graph*. ...##
###
Some Results on Greedy Embeddings in Metric Spaces

2009
*
Discrete & Computational Geometry
*

Geographic Routing is

doi:10.1007/s00454-009-9227-6
fatcat:asu4bmoiizcsvawzoyguug74qa
*a*family*of*routing*algorithms*that uses geographic point locations as addresses*for**the*purposes*of*routing. ... Here we resolve*a*conjecture*of*Papadimitriou and Ratajczak that every 3-connected planar*graph*admits*a*greedy embedding into*the*Euclidean plane. ... Acknowledgments We would like to thank Robert Kleinberg*for*introducing us to this problem and*for*many helpful discussions. ...##
###
Some Results on Greedy Embeddings in Metric Spaces

2008
*
2008 49th Annual IEEE Symposium on Foundations of Computer Science
*

Geographic Routing is

doi:10.1109/focs.2008.18
dblp:conf/focs/MoitraL08
fatcat:wsptm7s6tncn7i6jaokijkvify
*a*family*of*routing*algorithms*that uses geographic point locations as addresses*for**the*purposes*of*routing. ... Here we resolve*a*conjecture*of*Papadimitriou and Ratajczak that every 3-connected planar*graph*admits*a*greedy embedding into*the*Euclidean plane. ... Acknowledgments We would like to thank Robert Kleinberg*for*introducing us to this problem and*for*many helpful discussions. ...##
###
A simulated annealing algorithm for the maximum planar subgraph problem

2004
*
International Journal of Computer Mathematics
*

Two

doi:10.1080/00207160410001684352
fatcat:lyb2sijmnzfidjwajjcq7z2tf4
*algorithms*were given,*a*simple*algorithm*which runs in*linear*time*for*bounded-degree*graphs*with*a*ratio 7/18 and*a*more complicated*algorithm*with*a*ratio 4/9. ... We experimentally compare*the*new*algorithms*against*the*original simple*algorithm*. We also apply*the*new*algorithms**for*approximating*the*thickness and outerthickness*of**a**graph*. ... Acknowledgements*The*author thanks*the*anonymous referees*for*their valuable comments. ...##
###
Intersection Graphs of Non-crossing Paths
[article]

2020
*
arXiv
*
pre-print

*For*

*the*intersection

*graphs*

*of*NC paths

*of*

*a*tree, we characterize

*the*minimum connected dominating sets (leading to

*a*

*linear*time

*algorithm*to compute one). ...

*A*direct consequence

*of*our certifying

*algorithms*is

*a*

*linear*time

*algorithm*certifying

*the*presence/absence

*of*an induced claw (K_1,3) in

*a*chordal

*graph*. ...

*The*intersection

*graphs*

*of*subtrees

*of*

*a*

*cactus*were studied by Gavril [30] . So, one might consider

*the*NC-path/tree/

*cactus*-

*cactus*

*graphs*. ...

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