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An approach to the subgraph homeomorphism problem

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. ...

##
###
An exact algorithm for subgraph homeomorphism

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 ...

##
###
The existence of homeomorphic subgraphs in chordal graphs

1997
*
Applied Mathematics Letters
*

We also show how these results lead

doi:10.1016/s0893-9659(97)00027-x
fatcat:q4663fbr2vdzhkgsbj3u73gfoq
*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. ...##
###
Approximating the maximum clique minor and some subgraph homeomorphism problems

2007
*
Theoretical Computer Science
*

h or a

doi:10.1016/j.tcs.2006.12.021
fatcat:xieuhlle2ja7hea3pczirn4sfq
*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 ...##
###
Graph Minor Approach for Application Mapping on CGRAs

2014
*
ACM Transactions on Reconfigurable Technology and Systems
*

We design

doi:10.1145/2655242
fatcat:nitqwddh2jcwbng3qjdnf6nm34
*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 ...##
###
Mine 'Em All: A Note on Mining All Graphs
[chapter]

2016
*
Lecture Notes in Computer Science
*

We show that there are hereditary classes of graphs for which

doi:10.1007/978-3-319-40566-7_8
fatcat:x2kqtt2znff7dkvcpkgu574qee
*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*. ...##
###
A Practical Algorithm for Embedding Graphs on Torus

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 ...

##
###
A Practical Algorithm for Embedding Graphs on Torus

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 ...

##
###
On 3-cutwidth critical graphs

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. ...

##
###
A minimization version of a directed subgraph homeomorphism problem

2008
*
Mathematical Methods of Operations Research
*

We consider a special case of

doi:10.1007/s00186-008-0259-0
fatcat:a4xcfeipxjhafc65ighdu62yxm
*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*. ...##
###
THE OPEN PROBLEM OF FINDING A GENERAL CLASSIFICATION OF GEODETIC GRAPHS

2022
*
Zenodo
*

This note describes some open

doi:10.5281/zenodo.6861196
fatcat:3rfkbltzo5du5hfeuleubxmh3m
*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. ...##
###
Unified graph matching in Euclidean spaces

2010
*
2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
*

There are several variants of

doi:10.1109/cvpr.2010.5539859
dblp:conf/cvpr/McAuleyCC10
fatcat:ss2eqw3sgnag3evzeqnglnf2xq
*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. ...##
###
The subgraph homeomorphism problem for small wheels

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. ...

##
###
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

1970
*
Pacific Journal of Mathematics
*

However this

doi:10.2140/pjm.1970.34.501
fatcat:osrkbq74ybfy5iies4s5n52lxe
*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*. ...
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