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Two families of graphs satisfying the cycle basis interpolation property

1990
*
Discrete Mathematics
*

We construct

doi:10.1016/0012-365x(90)90271-i
fatcat:5xvnt6yfkzaszllvdmp5ao5pki
*two**families**of**graphs*with*the*chip, namely snake-*graphs*and kite-*graphs*. Lemma 1.1 [2]. ... Then G has*the**cycle**basis**interpolation**property*(chip) if for all integers c, c-CC CC+, there exists a*cycle**basis**of*length c. ...*Two**families**of**graphs*with*the*chip are known, namely complete*graphs*K, and wheels W, ([2] ). We prove that snake-*graphs*and kite-*graphs*also*satisfy**the*chip. ...##
###
Page 1328 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

A

*graph*G has*the**cycle**basis**interpolation**property*(cbip) if*the**family**of*all*cycle*bases*of*G*satisfies**the*cip. ...*the**cycle**basis**interpolation**property*. ...##
###
Cycle interpolation properties of graphs

1995
*
Discrete Mathematics
*

*The*length

*of*a set

*of*

*cycles*

*of*a

*graph*G is

*the*sum

*of*

*the*lengths

*of*its

*cycles*. ... G has

*the*

*cycle*

*basis*

*interpolation*

*property*(chip) if

*the*set

*of*all

*cycle*bases

*of*G

*satisfies*

*the*tip.

*The*chip we consider in Section 3. ... Snake-

*graph*S,, m 2 2, is a maximal outerplanar

*graph*whose

*cycle*

*graph*is a path

*of*m vertices.

*The*snake-

*graphs*form a

*family*

*of*

*graphs*

*satisfying*

*the*chip (see [4] ). ...

##
###
A Family of special outerplanar graphs with only one triangle satisfying the cycle basis interpolation property

1995
*
Discrete Mathematics
*

Then G has

doi:10.1016/0012-365x(94)00023-c
fatcat:qfjuec7xzbabtjh5ovvt53klxe
*the**cycle**basis**interpolation**property*(chip) if for all integers c, c-< c < c+, there exists a*cycle**basis**of*length c. ...*The*length*of*a*cycle**basis**of*a*graph*G is*the*sum*of**the*lengths*of*its*cycles*. Let c-, c+ be*the*lengths*of**the*minima1 and maxima1*cycle**basis*, respectively. ... Acknowledgement*The*author would like to thank Prof. Zhang Fuji, Prof. Guo Xiaofeng, Mr. Meng Jixiang and Mr. Shi Aifen for their helpful suggestions. ...##
###
Page 4737 of Mathematical Reviews Vol. , Issue 911
[page]

1991
*
Mathematical Reviews
*

(SA-CSIR-M)

*Two**families**of**graphs**satisfying**the**cycle**basis**interpolation**property*. Discrete Math. 84 (1990), no. 1, 39-46. Let G be a simple, undirected and connected*graph*. ... Then G has*the**cycle**basis**interpolation**property*(cbip) if for all integers c, c7 <c < ct, there exists a*cycle**basis**of*length c. F. Harary et al. ...##
###
Page 1518 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

*The*author’s main result is that four functions which are defined via hereditary and cohereditary

*properties*

*interpolate*over EDA-SET connectable

*families*

*of*subsets. ... It is a ternary operation defined for

*two*arbitrary pseudo-

*graphs*and

*the*third pseudo-

*graph*which has isomorphic copies in each

*of*

*the*first

*two*pseudo-

*graphs*. ...

##
###
Author index volume 84 (1990)

1990
*
Discrete Mathematics
*

On

doi:10.1016/0012-365x(90)90141-4
fatcat:hp5bwqzx3bapnmbeavvedpysma
*the*set coincidence game Rosenfeld, M.,*The*number*of**cycles*in 2-factors*of*cubic*graphs*(3) 241-254 (3) 303-307 ... .,*Two**families**of**graphs**satisfying**the**cycle**basis**interpolation**property*(1) 39-46 Jendrol, S., and M. ... Ordaz, Chvatal-Erd& conditions for paths and*cycles*in*graphs*and digraphs. ...##
###
Page 1652 of Mathematical Reviews Vol. , Issue 81E
[page]

1981
*
Mathematical Reviews
*

*The*

*basis*

*of*this paper is a notion which concerns a tuple

*of*distinct triangulation-free

*cycles*in

*the*line

*graph*

*of*

*the*bipartite

*graph*

*of*a matrix Y

*satisfying*

*two*special

*properties*and which

*the*author ... calls “a

*family*

*of*strongly connected polygons in

*the*adjoint

*graph*

*of*Y”. ...

##
###
Coarse-grid selection for parallel algebraic multigrid
[chapter]

1998
*
Lecture Notes in Computer Science
*

*of*heuistics designed to insme

*the*quality

*of*

*the*cease glids A prototype serial version

*of*

*the*algorithm is implemented, and tests are conducted to d&amine its effect on multigrid convergence, and AMG ... algorithms exist We introduce a paallel algorithm fol

*the*selection

*of*coals-glid points, a aucial component

*of*AMG, based on modifications

*of*certain paallel independent set algorithms and

*the*application ... eitha be coaxe points 01 must themselves depend on

*the*coarse points used to

*interpolate*ui

*The*coax grid is chosen to

*satisfy*

*two*criteria We enface P3 in order to insure good intapolation However, we ...

##
###
Graph Comparison via the Non-backtracking Spectrum
[article]

2018
*
arXiv
*
pre-print

We observe that

arXiv:1812.05457v1
fatcat:xbhozmoyabguvdaaiqhbonjlkq
*the**family**of*Watts-Strogatz*graphs*lie on a manifold in*the*non-backtracking spectral embedding and show how this metric can be used in a standard classification problem*of*empirical*graphs*...*The*comparison*of**graphs*is a vitally important, yet difficult task which arises across a number*of*diverse research areas including biological and social networks. ... Acknowledgments*The*authors would like to thank Renaud Lambiotte for useful discussion and both Renaud and Ebrahim Patel for a careful reading*of*early versions*of*this article. ...##
###
Algebraic multigrid(AMG) for saddle point systems from meshfree discretizations

2004
*
Numerical Linear Algebra with Applications
*

Since

doi:10.1002/nla.383
fatcat:ui73fx5furazlbmwsue2diojqe
*the*nodal*basis**property*is not*satisfied*in meshfree discretizations, it is difficult to handle essential boundary conditions. ... We adapt a variation*of**the*smoothed aggregation AMG method*of*Vaněk, Mandel & Brezina to this saddle point system. ... Acknowledgements*The*authors would like to thank*the*National Science Foundation for their generous support, and also*the*referees for their suggestions which have improved*the*presentation*of*this paper ...##
###
Further results on the Aanderaa-Rosenberg conjecture

1980
*
Journal of combinatorial theory. Series B (Print)
*

Some results on

doi:10.1016/0095-8956(80)90057-x
fatcat:j4zegjzoovb4pbyhy4r4azfhjy
*the*"evasiveness"*of**graph**properties*are obtained, extending*the*work*of*Rivest and Vuillemin. ... A new result allowing*interpolation*among n values is obtained, as are some stronger results on restricted classes*of**properties*. 85 ... ACKNOWLEDGMENTS*The*authors are indebted to R. Rivest and V. Boas for stimulating J. Griggs for many valuable suggestions and editorial assistance. ...##
###
Symmetric Computation (Invited Talk)

2020
*
Annual Conference for Computer Science Logic
*

In a

doi:10.4230/lipics.csl.2020.2
dblp:conf/csl/Dawar20
fatcat:jdwa32g6rnfxhh5ed7mnjayrwe
*graph*,*two*vertices may appear identical and therefore interchangeable while their concrete representations are distinguished by some feature (such as actual pointer values) that is hidden by*the*... For example, a widely used data model in*the*world*of*algorithm design is that*of**graphs*, which captures a collection*of*entities and their pairwise relationships. ...*of**graphs*with a Hamiltonian*cycle*, in contrast with*the*results*of*Yannakakis. ...##
###
The connectivity of the SEE-graph and AEE-graph for the connected spanning k-edge subgraphs of a graph

1998
*
Discrete Mathematics
*

These results give best lower bounds for

doi:10.1016/s0012-365x(97)00057-5
fatcat:6lcwgffsnbanlectymq3uas4sa
*the*numbers*of*times that many*interpolating*invariant values are attained over*the*set*of*all connected spanning k-edge subgraphs*of*a*graph*G. ... In this paper, we show that*the*connectivity*of**the*SEE-*graph*for*the*connected spanning k-edge subgraphs*of*a*graph*G is equal to*the*minimum degree*of**the*SEE-*graph*, and*the*connectivity*of**the*AEE-*graph*... Acknowledgements*The*author would like to thank*the*referees for their helpful comments. ...##
###
Interpolation theorems for domination numbers of a graph

1998
*
Discrete Mathematics
*

An integer-valued

doi:10.1016/s0012-365x(98)00108-3
fatcat:wkbvsanizfgcfhkho26chvemcm
*graph*function n is an*interpolating*function if for every connected*graph*G, z(Y(G)) is a set*of*consecutive integers, where J(G) is*the*set*of*all spanning trees*of*G. ...*The**interpolating*character*of*a number*of*domination related parameters is considered. (~ 1998 Elsevier Science B.V. All right reserved ...*interpolating*function with respect to*the**family**of*spanning trees*of*a*graph*. ...
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