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The Connectivities of Leaf Graphs of Sets of Points in the Plane

2001
*
Tokyo Journal of Mathematics
*

Let U be

doi:10.3836/tjm/1255958194
fatcat:fwgv6okcfrgkvjlg754elvxftm
*a*set*of*n points in*the*plane. If no three points are collinear, then we s*a*y ... Broersma and Li Xueliang,*The**connectivity**of**the**leaf*-*exchange*ane*spanning**tree**graph**of**a**graph*, ARS Comb. 43 (1996) , 225-231 [2] E. Campo and V. ... In this paper, we study*a**spanning*subgraph*of**the**tree**graph*on U, called*a**leaf**graph*. ...##
###
Enumeration of Spanning Trees Using Edge Exchange with Minimal Partitioning
[article]

2014
*
arXiv
*
pre-print

While MP algorithm uses

arXiv:1407.0699v1
fatcat:hlkt5d5g7ndbpb3u5ph2x4nhiq
*a*computational*tree**graph*to traverse all possible*spanning**trees*by*the*edge*exchange*technique, it has two unique properties compared to previous algorithms. ... Practically, and as*a*result*of*this property,*the*interface between*the*two partitions*of**the**spanning**tree*during edge*exchange*has to be maintained from one side only. ... (*a*) shows*a**graph**The*parent*of**a*type 2*spanning**tree*is*the**spanning**tree*formed by*exchanging**the**leaf*pilot pair*of**the**tree*with*the**leaf*pair that has*the*same node component and with edge that has ...##
###
Page 2775 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

*A*variation on

*the*

*leaf*-

*exchange*

*spanning*

*tree*

*graph*appeared in recent work on basis

*graphs*

*of*branching greedoids. ... We characterize

*the*

*graphs*which have

*a*

*connected*

*leaf*-

*exchange*

*spanning*

*tree*

*graph*and give

*a*lower bound on

*the*

*connectivity*

*of*7)(G) for

*a*3-

*connected*

*graph*G.” 97e:05129 05C40 05C38 Gao, Jingzhen ( ...

##
###
Spanning Trees: A Survey

2010
*
Graphs and Combinatorics
*

In this paper, we give

doi:10.1007/s00373-010-0973-2
fatcat:y6w7gmq5kfdula4heioxocsn3a
*a*survey*of**spanning**trees*. ... We mainly deal with*spanning**trees*having some particular properties concerning*a*hamiltonian properties, for example,*spanning**trees*with bounded degree, with bounded number*of*leaves, or with bounded ... Acknowledgements*The*authors would like to thank*the*referees for their helpful comments and corrections. ...##
###
On the Structure of the Graph of Unique Symmetric Base Exchanges of Bispanning Graphs
[article]

2016
*
arXiv
*
pre-print

*The*operation

*of*symmetrically swapping two edges between

*the*

*trees*, such that

*the*result is

*a*different pair

*of*disjoint

*spanning*

*trees*, is called an edge

*exchange*or

*a*symmetric base

*exchange*. ...

*The*

*graph*

*of*symmetric base

*exchanges*

*of*

*a*bispanning

*graph*contains

*a*vertex for every valid pair

*of*disjoint

*spanning*

*trees*, and edges between them to represent all possible edge

*exchanges*. ... Lemma 4 . 4 13 (leafUEs: unique

*exchanges*due to

*leaf*edges) If (S, T ) ∈ V τ (G) is

*a*pair

*of*disjoint

*spanning*

*trees*

*of*

*a*bispanning

*graph*G = (V, E, δ), and v ∈ V is

*a*

*leaf*in

*the*

*tree*-

*graph*G[S] incident ...

##
###
Fixed Parameter Evolutionary Algorithms and Maximum Leaf Spanning Trees: A Matter of Mutation
[chapter]

2010
*
Parallel Problem Solving from Nature, PPSN XI
*

We investigate

doi:10.1007/978-3-642-15844-5_21
dblp:conf/ppsn/KratschLNO10
fatcat:byxjfluezzgydcmzdrxqmcskda
*the*NP-hard problem*of*computing*a**spanning**tree*that has*a*maximal number*of*leaves by evolutionary algorithms in*the*context*of*fixed parameter tractability (FPT) where*the*maximum number ... Investigating two common mutation operators, we show that an operator related to*spanning**tree*problems leads to an FPT running time in contrast to*a*general mutation operator that does not have this property ... Given an undirected*connected**graph*G = (V, E),*the*goal is to find*a**spanning**tree*T **of*G such that*the*number*of*leaves is maximal. ...##
###
The connectivity of the basis graph of a branching greedoid

1992
*
Journal of Graph Theory
*

*A*result

*of*Korte and L O V~S Z states that

*the*basis

*graph*

*of*every 2connected greedoid is

*connected*. ... We prove that

*the*basis

*graph*

*of*every 3-

*connected*branching greedoid is (6 -1)-

*connected*, where 6 is

*the*minimum in-degree (disregarding

*the*root)

*of*

*the*underlying rooted directed (mu1ti)

*graph*. ... This also implies that every

*spanning*

*tree*

*of*

*a*2-

*connected*rooted

*graph*can be changed into

*a*given second one by successively

*exchanging*

*a*single

*leaf*in every step. ...

##
###
A 2k-Vertex Kernel for Maximum Internal Spanning Tree
[article]

2014
*
arXiv
*
pre-print

We consider

arXiv:1412.8296v1
fatcat:khoxp3wr5vbgrm4nbgs4tnrj6y
*the*parameterized version*of**the*maximum internal*spanning**tree*problem, which, given an n-vertex*graph*and*a*parameter k, asks for*a**spanning**tree*with at least k internal vertices. ... Our algorithm applies first*a*greedy procedure consisting*of**a*sequence*of*local*exchange*operations, which ends with*a*local-optimal*spanning**tree*, and then uses this special*tree*to find*a*reducible ... Introduction*A**spanning**tree**of**a**connected**graph*G is*a*subgraph that includes all*the*vertices*of*G and is*a**tree*. ...##
###
An approximation algorithm for the maximum leaf spanning arborescence problem

2010
*
ACM Transactions on Algorithms
*

We present an O( √ opt)-approximation algorithm for

doi:10.1145/1798596.1798599
fatcat:vnwi5bkzinf7fgvkjojbl7j2sy
*the*maximum*leaf**spanning*arborescence problem, where opt is*the*number*of*leaves in an optimal*spanning*arborescence. ...*The*result is based upon an O(1)-approximation algorithm for*a*special class*of*directed*graphs*called willows. ...*A*natural question is then to find*a**spanning**tree*T in*a*undirected*graph*G containing*the*maximum number*of*leaves. ...##
###
The Connectivities of Leaf Graphs of 2-Connected Graphs

1999
*
Journal of combinatorial theory. Series B (Print)
*

Given

doi:10.1006/jctb.1998.1895
fatcat:2jb7ebylhfeipld2su4pwqx2de
*a**connected**graph*G, denote by V*the*family*of*all*the**spanning**trees**of*G. ... Define an adjacency relation in V as follows:*the**spanning**trees*t and t$ are said to be adjacent if for some vertex u # V, t&u is*connected*and coincides with t$&u. ... ACKNOWLEDGMENTS*The*authors thank Professor S. Matsumoto and Professor Y. Egawa for his helpful advice. ...##
###
Spanning tree with many leaves in quadratic graph

2013
*
International Journal of Research Studies in Computing
*

For

doi:10.5861/ijrsc.2014.603
fatcat:zemhfmyrlvdxtpatenlqclq22u
*a**connected**graph*G let L(G) denote*the*maximum number*of*leaves in any*spanning**tree**of*G. ... Another large class*of*properties deals with*the*structure*of**the*leaves*of**the**spanning**tree*. ... As we know*tree*is*a**connected**graph*, in*the*last steps*of*this algorithm we*connect*T and*the*isolated vertices (which does not satisfy inequality) and return*the**connected**spanning**tree*TA. ...##
###
Distributed algorithms for finding and maintaining a k-tree core in a dynamic network

2003
*
Information Processing Letters
*

In this paper first we propose

doi:10.1016/s0020-0190(03)00365-x
fatcat:ljyfmnia35h2bhmmpcczseecry
*a*distributed algorithm for constructing*a*rooted*spanning**tree**of**a*dynamic*graph*such that root*of**the**tree*is located near*the*center*of**the**graph*. ... In*the*next stage these*trees*are*connected*to form*a*single rooted*tree*. ... For*a**graph**of*this kind finding*a*rooted*spanning**tree*itself can be challenging. ...##
###
An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem

2009
*
Applied Soft Computing
*

Introduction Given an undirected,

doi:10.1016/j.asoc.2008.09.001
fatcat:rxfkzkvqczhqtibkrjmqjasmry
*connected*, weighted*graph*with n nodes and*a*positive integer 'ð2 ' < n*À*1Þ,*the**leaf*-constrained minimum*spanning**tree*(LCMST) problem seeks on this*graph**a**spanning*... Julstrom [4] observed that for ' ¼ 0:6n, ML finds lower-weight Given an undirected,*connected*, weighted*graph*,*the**leaf*-constrained minimum*spanning**tree*(LCMST) problem seeks on this*graph**a**spanning*...##
###
The Chartrand-Schuster conjecture: Graphs with unique distance trees are regular

1977
*
Journal of combinatorial theory. Series B (Print)
*

*A*distance

*tree*T is

*a*

*spanning*

*tree*

*of*G which further satisfies

*the*condition that for some vertex E, d&, u) = dr(u, u) for aI U, where d&v, u) denotes

*the*distance

*of*u from v in

*the*

*graph*G. ... Let G be

*a*finite

*connected*

*graph*with no cut vertex. ... Let T1 and T, be two distance

*trees*at

*a*vertex x

*of*

*a*

*connected*

*graph*G. Then one can pass from T1 to T, in

*a*$nite sequence

*of*"

*exchanges*." Proof. Assume T, # T, . ...

##
###
Reconfiguration of Spanning Trees with Many or Few Leaves

2020
*
European Symposium on Algorithms
*

Since

doi:10.4230/lipics.esa.2020.24
dblp:conf/esa/BousquetI0MOSW20
fatcat:4sey3bvc7jeb7azxzh4peh2dxu
*spanning**trees*form*a*matroid, one can indeed transform*a**spanning**tree*into any other via*a*sequence*of*edge flips, as observed in [Takehiro Ito et al., 2011]. ... Let G be*a**graph*and T₁,T₂ be two*spanning**trees**of*G. We say that T₁ can be transformed into T₂ via an edge flip if there exist two edges e ∈ T₁ and f in T₂ such that T₂ = (T₁⧵e) ∪ f. ...*A**spanning**tree*T*of*G is frozen if all*the**spanning**trees*in its*connected*component*of**the*reconfiguration*graph*have*the*same internal nodes. Claim 22 (*). Let T be*a**spanning**tree**of*G. ...
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