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Page 40 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
It is optimal for graphs that satisfy m > log’ n.  ...  Algorithms 16 (1994), no. 2, 190-217. The best currently known parallel algorithm for finding the con- nected components of an undirected graph was given by Cole and Vishkin in 1991.  ... 

One- and two-page crossing numbers for some types of graphs

Hongmei He, Ana Sălăgean, Erkki Mäkinen
2010 International Journal of Computer Mathematics  
In this paper, we derive the exact one-page crossing numbers for four-row meshes, present a new proof for the one-page crossing numbers of Halin graphs, and derive the exact two-page crossing numbers for  ...  We also give explicit constructions of the optimal drawings for each kind of graphs.  ...  In the new version, we prove the upper bound of one-page crossing number for a Halin graph by providing an algorithm to construct a drawing based on a special Hamiltonian cycle for the Halin graph and  ... 
doi:10.1080/00207160802524747 fatcat:7jouokp2rbgilig2aphla4sccq

A Linear Time Algorithm for the 3-neighbour Traveling Salesman Problem on Halin graphs and extensions [article]

Brad Woods, Abraham Punnen, Tamon Stephen
2017 arXiv   pre-print
We define a restricted version of QTSP, the k-neighbour TSP (TSP(k)), and give a linear time algorithm to solve TSP(k) on a Halin graph for k≤ 3.  ...  This algorithm can be extended to solve TSP(k) on any fully reducible class of graphs for any fixed k in polynomial time. This result generalizes corresponding results for the standard TSP.  ...  An O(n) algorithm to solve TSP(3) on Halin graphs is given in Section 4.1, which can be extended to obtain an O(n2 (k−1)/2 ) algorithm for TSP(k).  ... 
arXiv:1504.02151v5 fatcat:sgki4xxk45fp7jhegekflsiuhe

Page 5309 of Mathematical Reviews Vol. , Issue 84m [page]

1984 Mathematical Reviews  
Author’s summary: “We propose an algorithm for obtaining a Hamiltonian path from a shortest spanning tree of a complete 84m:90049  ...  5309 algorithm is defined for the generation of lower and upper bounds of the optimal objective value, and conditions are given for the algorithm to produce an optimal solution, extending results of B.  ... 

Various heuristic algorithms to minimise the two-page crossing numbers of graphs

Hongmei He, Ana Sălăgean, Erkki Mäkinen, Imrich Vrt'o
2015 Open Computer Science  
We conjecture that the optimal two-page drawing of a graph represents the planar drawing of the graph.  ...  Especially, the neural network model for edge allocation is combined for the first time with various one-page algorithms.  ...  We also proposed a hybrid algorithm (AVSDF_EP), which directly assign edges into pages while placing the vertices on the circle in the AVSDF algorithm.  ... 
doi:10.1515/comp-2015-0004 fatcat:gmxkbqolvrhkrljq3xpjly435i

Parallel O(log n) time edge-colouring of trees and Halin graphs

Alan M. Gibbons, Amos Israeli, Wojciech Rytter
1988 Information Processing Letters  
In the case of Halin graphs with a maximum degree of three, the colouring algorithm automatically finds every Hamiltonian cycle of the graph.  ...  In the case of Halin graphs with a maximum degree of three, the colouring algorithm automatically finds every Hamiltonian cycle of the graph.  ...  Clearly C is a Hamiltonian cycle. This completes the proof of the theorem. the algorithm EDGECOLOUR provides every Hamiltonian cycle of the Halin graph. Proof Let G be a Halin graph with A=3.  ... 
doi:10.1016/0020-0190(88)90080-4 fatcat:xe3ymnlkpjcp3llqdbmkzamwlq

A survey of very large-scale neighborhood search techniques

Ravindra K. Ahuja, Özlem Ergun, James B. Orlin, Abraham P. Punnen
2002 Discrete Applied Mathematics  
Therefore, a practical approach for solving such problems is to employ heuristic (approximation) algorithms that can ÿnd nearly optimal solutions within a reasonable amount of computation time.  ...  A critical issue in the design of a neighborhood search algorithm is the choice of the neighborhood structure, that is, the manner in which the neighborhood is deÿned.  ...  The fourth author was supported by NSERC Grant OPG0170381. References [1] E. Aarts, J.K. Lenstra, Local Search in Combinatorial Optimization, Wiley, New York, 1997.  ... 
doi:10.1016/s0166-218x(01)00338-9 fatcat:q75y577kdbcdffh46dafrb47uq

Persistency in the Traveling Salesman Problem on Halin graphs

Vladimír Lacko
2000 Discussiones Mathematicae Graph Theory  
For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency  ...  partition E All , E Some , E N one of the edge set E, where: E All = {e ∈ E, e belongs to all optimum solutions}, E N one = {e ∈ E, e does not belong to any optimum solution} and E Some = {e ∈ E, e belongs  ...  A polynomial algorithm for finding one optimum solution of TSP on Halin graphs was given in [4] .  ... 
doi:10.7151/dmgt.1122 fatcat:4jz4wpmlyvddtcap62i6pkulju

On Halin subgraphs and supergraphs

S.B. Horton, R.Gary Parker
1995 Discrete Applied Mathematics  
The first pertains to the problem of finding Halin subgraphs while the second is a supergraph version which asks if a given graph is a subgraph of any Hahn graph.  ...  Both of these problems are shown to be hard which, in turn, provides somewhat damaging evidence relative to the veracity of heuristic approaches employing Halin graphs as approximations.  ...  Readers are directed to references such as [l 1, 123 for appropriate coverage (e.g., all Halin graphs are Hamiltonian, 1-Hamiltonian, bicritical, etc.).  ... 
doi:10.1016/0166-218x(93)e0131-h fatcat:ivuhuryf7bff5cxq6b7ahj4rmq

Halin graphs are 3-vertex-colorable except even wheels [article]

A. Kapanowski, A. Krawczyk
2019 arXiv   pre-print
The algorithms are implemented in Python using the graphtheory package. Generators of random Halin graphs (general or cubic) are included.  ...  A Halin graph is a graph obtained by embedding a tree having no nodes of degree two in the plane, and then adding a cycle to join the leaves of the tree in such a way that the resulting graph is planar  ...  However, in the case of Halin graphs an optimal coloring can be found in linear time. A short description of the coloring algorithm is the following. Let H = T ∪ C be a Halin graph.  ... 
arXiv:1903.02904v1 fatcat:hve6e6dqa5c45nvjxz3mo4rlhm

Page 2139 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
This problem includes, as special cases, the problem of finding a Hamiltonian path and the problem of determining the depth of a flow graph.  ...  This paper gives a polynomial-time algorithm to solve the simple-path problem, where the input is a 2-decomposable flow graph.  ... 

Solving problems on recursively constructed graphs

Richard B. Borie, R. Gary Parker, Craig A. Tovey
2008 ACM Computing Surveys  
Fast algorithms can be created for many graph problems when instances are confined to classes of graphs that are recursively constructed.  ...  The notion of composition typically permitted in the context of k-terminal graphs can be described in a more formal way.  ...  Closure function for Hamiltonian path algorithm 12.4 Algorithm for Hamiltonian path in a cliquewidth-k graph Define: Again, let [k] denote the set of integers {1, 2, . . . , k}.  ... 
doi:10.1145/1456650.1456654 fatcat:i4l5pratpzb35prq4df7ar3pka

Author index

1987 Discrete Applied Mathematics  
Tokura, An optimal time algorithm for the k-vertexconnectivity unweighted augmentation problem for rooted directed trees (1,2) 67-105 Maamoun, M., and H.  ...  Fujishige, Finding a homotopy base for directed paths in an acyclic graph (1,2) 157-162 Nishida, T., see H.  ... 
doi:10.1016/0166-218x(87)90035-7 fatcat:wzoft6womzg5vl3qmj2ocab34m

Page 7336 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Algorithms are presented to determine the least deviant path. The fastest algorithm runs in O(|E|'-7), in the worst case.  ...  Summary: “A least deviant path between two vertices in a weighted graph is defined as a path that minimizes the difference between the largest and smallest edge weights on the path.  ... 

Page 26 of Mathematical Reviews Vol. 49, Issue 1 [page]

1975 Mathematical Reviews  
49 #141-147 It is shown that if a graph G is the sum of n Hamiltonian circuits then the product graph Gx G is the sum of 2n Hamiltonian circuits. L. V.  ...  Quintas (New York) Nakamori, Mario 141 A note on the optimality of some all-shortest-path algo- rithms. J. Operations Res. Soc. Japan 15 (1972), 201-204.  ... 
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