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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

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 ...

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

2017
*
arXiv
*
pre-print

We define a restricted version of QTSP,

arXiv:1504.02151v5
fatcat:sgki4xxk45fp7jhegekflsiuhe
*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). ...##
###
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

2015
*
Open Computer Science
*

We conjecture that

doi:10.1515/comp-2015-0004
fatcat:gmxkbqolvrhkrljq3xpjly435i
*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*. ...##
###
Parallel O(log n) time edge-colouring of trees and Halin graphs

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. ...

##
###
A survey of very large-scale neighborhood search techniques

2002
*
Discrete Applied Mathematics
*

Therefore, a practical approach

doi:10.1016/s0166-218x(01)00338-9
fatcat:q75y577kdbcdffh46dafrb47uq
*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. ...##
###
Persistency in the Traveling Salesman Problem on Halin graphs

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] . ...

##
###
On Halin subgraphs and supergraphs

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.). ...

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

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*. ...

##
###
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

2008
*
ACM Computing Surveys
*

Fast

doi:10.1145/1456650.1456654
fatcat:i4l5pratpzb35prq4df7ar3pka
*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}. ...##
###
Author index

1987
*
Discrete Applied Mathematics
*

Tokura, An

doi:10.1016/0166-218x(87)90035-7
fatcat:wzoft6womzg5vl3qmj2ocab34m
*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. ...##
###
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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