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

C. Meloni
2001 Electronic Notes in Discrete Mathematics  
Given a graph G =  ...  Skupieà 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.  ... 
doi:10.1016/s1571-0653(05)80070-8 fatcat:djcokupptreghaampyli2ofqni

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

Paolo Detti, Carlo Meloni
2004 Discrete Applied Mathematics  
Given a graph G =  ...  Skupieà 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.  ... 
doi:10.1016/s0166-218x(03)00441-4 fatcat:po4fekjolfbphjz6uyzjraxwfa

Algorithms for Maximum Internal Spanning Tree Problem for Some Graph Classes [article]

Gopika Sharma, Arti Pandey, Michael C. Wigal
2021 arXiv   pre-print
In this paper, we propose 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.  ... 
arXiv:2112.02248v2 fatcat:sypp5xi27jhs3mfh3cl72g4rxy

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

D. S. Franzblau, A. Raychaudhuri
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  ... 
doi:10.1017/s1446181100013894 fatcat:barywqu755d5heksyrflp6snzy

Computing compatible tours for the symmetric traveling salesman problem

Matteo Fortini, Adam N. Letchford, Andrea Lodi, Klaus M. Wenger
2010 Mathematical Programming Computation  
We then describe 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.  ... 
doi:10.1007/s12532-010-0021-5 fatcat:x7dryg27ifecpi3hplp2fmkcdm

Vertex and Tree Arboricities of Graphs

Gerard J. Chang, Chiuyuan Chen, Yaping Chen
2004 Journal of combinatorial optimization  
This paper studies 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.  ... 
doi:10.1023/b:joco.0000038912.82046.17 fatcat:zq75b47o3ffjjkd7s2r6r76gde

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, 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.  ... 
doi:10.1016/s0166-218x(03)00669-3 fatcat:nplxrn6oxbdvpf2t3cyzo7wugu

Peeling and Nibbling the Cactus: Subexponential-Time Algorithms for Counting Triangulations and Related Problems

Dániel Marx, Miltzow Tillmann, Marc Herbstritt
2016 International Symposium on Computational Geometry  
Based on 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.  ... 
doi:10.4230/lipics.socg.2016.52 dblp:conf/compgeom/MarxM16 fatcat:bdpig53xlfdg3hbri3corqqcim

Separating maximally violated comb inequalities in planar graphs [chapter]

Lisa Fleischer, Éva Tardos
1996 Lecture Notes in Computer Science  
Our 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.  ... 
doi:10.1007/3-540-61310-2_35 fatcat:qvegfj6eondkxmvt52tfxaagve

Some Results on Greedy Embeddings in Metric Spaces

Tom Leighton, Ankur Moitra
2009 Discrete & Computational Geometry  
Geographic Routing is 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.  ... 
doi:10.1007/s00454-009-9227-6 fatcat:asu4bmoiizcsvawzoyguug74qa

Some Results on Greedy Embeddings in Metric Spaces

Ankur Moitra, Tom Leighton
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science  
Geographic Routing is 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.  ... 
doi:10.1109/focs.2008.18 dblp:conf/focs/MoitraL08 fatcat:wsptm7s6tncn7i6jaokijkvify

A simulated annealing algorithm for the maximum planar subgraph problem

Timo Poranen
2004 International Journal of Computer Mathematics  
Two 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.  ... 
doi:10.1080/00207160410001684352 fatcat:lyb2sijmnzfidjwajjcq7z2tf4

Intersection Graphs of Non-crossing Paths [article]

Steven Chaplick
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.  ... 
arXiv:1907.00272v2 fatcat:paeipvyuk5gmxl6wcunfatj56a
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