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An approach to the subgraph homeomorphism problem

Takao Asano
1985 Theoretical Computer Science  
The subgraph homeomorphism problem for a fixed pattern graph H is stated as follows:. given an input graph G = (V, E), determine whether G has a subgraph homeomorphic to H.  ...  Next, we present an O(l V12)-time algorithm for actually finding a subgraph of G homeomorphic to K3,3 if G has such a subgraph.  ...  Approach to the subgraph homeomorphism problem 261 Fig. 8 . 8 Graphs Wnel, K3,n_3, (P2u K,)+K,_,, P3+L3, and K,+K,_, (in the case of n = 8). Lemma 5.7.  ... 
doi:10.1016/0304-3975(85)90222-1 fatcat:aesoedd3vjf3pcadufct7epd4a

An exact algorithm for subgraph homeomorphism

Andrzej Lingas, Martin Wahlen
2009 Journal of Discrete Algorithms  
The subgraph homeomorphism problem is to decide if there is an injective mapping of the vertices of a pattern graph into vertices of a host graph so that the edges of the pattern graph can be mapped into  ...  The restriction of subgraph homeomorphism where an injective mapping of the vertices of the pattern graph into vertices of the host graph is already given in the input instance is termed fixed-vertex subgraph  ...  Acknowledgements The authors are grateful to Fedor Fomin for inspiration, to Andreas Björklund and Thore Husfeldt for informing about their recent results, and to unknown referees for valuable comments  ... 
doi:10.1016/j.jda.2008.10.003 fatcat:nh7hy24fdrcrlbv242dpjtlabm

The existence of homeomorphic subgraphs in chordal graphs

C.R. Subramanian, C.E. Veni Madhavan
1997 Applied Mathematics Letters  
We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some special classes of pattern graphs.  ...  We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to Kn (n >_ 3), Km,n (m, n >_ 2), and wheels Wr (r _> 3).  ...  Algorithms for the Fixed Subgraph Homeomorphism Problem on Chordal Graphs The Subgraph Homeomorphism Problem SHP is as follows.  ... 
doi:10.1016/s0893-9659(97)00027-x fatcat:q4663fbr2vdzhkgsbj3u73gfoq

Approximating the maximum clique minor and some subgraph homeomorphism problems

Noga Alon, Andrzej Lingas, Martin Wahlen
2007 Theoretical Computer Science  
h or a subgraph homeomorphic to K h , respectively, as well as the problem of finding the corresponding subgraphs.  ...  We consider the "minor" and "homeomorphic" analogues of the maximum clique problem, i.e., the problems of determining the largest h such that the input graph (on n vertices) has a minor isomorphic to K  ...  Acknowledgments We are grateful to Andreas Björklund for bringing Fact 9 to our attention, and to Anders Dessmark and Andrzej Proskurowski for sharing their knowledge on subgraph embedding algorithms for  ... 
doi:10.1016/j.tcs.2006.12.021 fatcat:xieuhlle2ja7hea3pczirn4sfq

Graph Minor Approach for Application Mapping on CGRAs

Liang Chen, Tulika Mitra
2014 ACM Transactions on Reconfigurable Technology and Systems  
We design an exact graph minor testing approach that exploits the unique properties of both the data flow graph and the routing resource graph to significantly prune the search space.  ...  We formalize the CGRA mapping problem as a graph minor containment problem.  ...  We formalize the CGRA mapping problem as restricted graph minor containment of the data flow graph representing the computation kernel in the modulo routing resource graph representing the CGRA architecture  ... 
doi:10.1145/2655242 fatcat:nitqwddh2jcwbng3qjdnf6nm34

Mine 'Em All: A Note on Mining All Graphs [chapter]

Ondřej Kuželka, Jan Ramon
2016 Lecture Notes in Computer Science  
We show that there are hereditary classes of graphs for which the complexity of this problem depends on the order in which the graphs should be enumerated (e.g. from frequent to infrequent or from small  ...  For instance, the problem can be solved with polynomial delay for databases of planar graphs when the enumerated graphs should be output from large to small but it cannot be solved even in incremental-polynomial  ...  It is easy to see that we could then use an incremental-polynomial time algorithm for the ALL F →I problem to solve the Hamitonian cycle problem.  ... 
doi:10.1007/978-3-319-40566-7_8 fatcat:x2kqtt2znff7dkvcpkgu574qee

A Practical Algorithm for Embedding Graphs on Torus

Jiahua Yu, Qian-Ping Gu
2016 International Journal of Networking and Computing  
To develop an efficient practical tool for embedding graphs on the torus, we propose a new exponential time algorithm for embedding graphs on the torus.  ...  It is required to embed a graph on the torus for solving many application problems such as VLSI design, graph drawing and so on.  ...  Acknowledgment The authors thank Skoda for his improved version of NM Algorithm and the code (in JAVA) of the algorithm, and thank Mohar and Skoda for their discussions on the problem of embedding graphs  ... 
doi:10.15803/ijnc.6.2_149 fatcat:dqvtn3hkeng4nnlljyxtjs2ety

A Practical Algorithm for Embedding Graphs on Torus

Jiahua Yu, Qian-Ping Gu
2015 2015 Third International Symposium on Computing and Networking (CANDAR)  
To develop an efficient practical tool for embedding graphs on the torus, we propose a new exponential time algorithm for embedding graphs on the torus.  ...  It is required to embed a graph on the torus for solving many application problems such as VLSI design, graph drawing and so on.  ...  Acknowledgment The authors thank Skoda for his improved version of NM Algorithm and the code (in JAVA) of the algorithm, and thank Mohar and Skoda for their discussions on the problem of embedding graphs  ... 
doi:10.1109/candar.2015.10 dblp:conf/ic-nc/YuG15 fatcat:lktzmplxt5ejxeedtbgcskhhae

On 3-cutwidth critical graphs

Yixun Lin, Aifeng Yang
2004 Discrete Mathematics  
The cutwidth problem has been motivated from both applied and theoretical points of view.  ...  The characterization of forbidden subgraphs or critical graphs is always interesting in the study of a graph-theoretic parameter.  ...  Acknowledgements The authors would like to thank the referees for their comments on improving the representation of the paper.  ... 
doi:10.1016/j.disc.2003.06.012 fatcat:6btteq7ujzfa3bvghi3xikjzpm

A minimization version of a directed subgraph homeomorphism problem

Janina A. Brenner, Sándor P. Fekete, Jan C. van der Veen
2008 Mathematical Methods of Operations Research  
We consider a special case of the directed subgraph homeomorphism or topological minor problem, where the host graph has a specific regular structure.  ...  In this application domain, the task is to simultaneously schedule, bind and route a so-called data-flow graph, where vertices represent operations and arcs stand for data dependencies between the operations  ...  Directed subgraph homeomorphism problem The SSBR problem is a special case of the Directed Subgraph Homeomorphism (DSH) problem.  ... 
doi:10.1007/s00186-008-0259-0 fatcat:a4xcfeipxjhafc65ighdu62yxm

THE OPEN PROBLEM OF FINDING A GENERAL CLASSIFICATION OF GEODETIC GRAPHS

C.E. Frasser
2022 Zenodo  
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs.  ...  This permitted us to create a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one.  ...  of complete graphs, started to be an inherent part of the problem of characterization.  ... 
doi:10.5281/zenodo.6861196 fatcat:3rfkbltzo5du5hfeuleubxmh3m

Unified graph matching in Euclidean spaces

Julian J. McAuley, Teofilo de Campos, Tiberio S. Caetano
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
There are several variants of the matching problem, concerned with isometries, isomorphisms, homeomorphisms, and node attributes; different approaches exist for each variant.  ...  In this paradigm, the extent to which our datasets reveal isometries, isomorphisms, homeomorphisms, and other properties is automatically accounted for in the learning process so that any such specific  ...  Acknowledgements The research leading to these results has received funding from the EC FP7 grant 216529 (PinView), as well as EP-SRC/UK grant EP/F069626/1, ACASVA.  ... 
doi:10.1109/cvpr.2010.5539859 dblp:conf/cvpr/McAuleyCC10 fatcat:ss2eqw3sgnag3evzeqnglnf2xq

The subgraph homeomorphism problem for small wheels

Graham Farr
1988 Discrete Mathematics  
The subgraph homeomorphism problem, where the pattern graph is a wheel with four or five spokes, is studied.  ...  Efficient algorithms are describ& for these cases of the subgraph homeomorphism problem.  ...  Thus, in the sense of polynomial time solvability versus NP-completeness, the subgraph homeomorphism problem is now completely solved.  ... 
doi:10.1016/0012-365x(88)90066-0 fatcat:b553jkcdsvhsfepc244gxavzha

Page 719 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
A nice drawing of a sparse nonplanar graph can be found by determining a maximum planar subgraph (which is an NP-hard problem) and augmenting an embedding of this graph.  ...  In the combinatorial approach, the final image is the composition of a sequence of local homeomorphic deformations. The paper is divided into 8 sections.  ... 

Intersection representations of graphs by arcs

Peter Renz
1970 Pacific Journal of Mathematics  
However this approach merely suggests how such a calculation might proceed without giving details or suggesting the size of the problem.  ...  A section graph of a graph H is a subgraph K of H such that the inclusion map from K to H is a graph homeomorphism.  ... 
doi:10.2140/pjm.1970.34.501 fatcat:osrkbq74ybfy5iies4s5n52lxe
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