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### Two families of graphs satisfying the cycle basis interpolation property

Elzbieta B. Jarrett
1990 Discrete Mathematics
We construct two families of graphs with the chip, namely snake-graphs and kite-graphs. Lemma 1.1 .  ...  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, ( ). 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

Wl̵lodzimierz Ulatowski
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  ).  ...

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

Liu Yan
1995 Discrete Mathematics
Then G has 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 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]

Andrew J. Cleary, Robert D. Falgout, Van Emden Henson, Jim E. Jones
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]

Andrew Mellor, Angelica Grusovin
2018 arXiv   pre-print
We observe that 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

K. H. Leem, S. Oliveira, D. E. Stewart
2004 Numerical Linear Algebra with Applications
Since 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

D.J Kleitman, D.J Kwiatkowski
1980 Journal of combinatorial theory. Series B (Print)
Some results on 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)

Anuj Dawar, Michael Wagner
2020 Annual Conference for Computer Science Logic
In a 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

Xueliang Li
1998 Discrete Mathematics
These results give best lower bounds for 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

Jerzy Topp, Preben Dahl Vestergaard
1998 Discrete Mathematics
An integer-valued 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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