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Hypergraph Isomorphism for Groups with Restricted Composition Factors

Daniel Neuen, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
In particular, this gives an isomorphism test for graphs of Euler genus at most g running in time n^O((log g)^c).  ...  As an application of this result, we obtain, for example, an algorithm testing isomorphism of graphs excluding K_{3,h} as a minor in time n^O((log h)^c).  ...  In particular, this gives an isomorphism test for graphs of Euler genus at most g running in time n O((log g) c ) .  ... 
doi:10.4230/lipics.icalp.2020.88 dblp:conf/icalp/Neuen20 fatcat:xa3qrjq3qzezrorjnkg7sdysqe

A practical algorithm for the computation of the genus

Gunnar Brinkmann
2022 Ars Mathematica Contemporanea  
We describe a practical algorithm to compute the (orientable) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms.  ...  The aim of this algorithm is to be fast enough for many applications instead of focusing on the theoretical asymptotic complexity.  ...  For these tests, for multi genus no lower bound for the genus was computed.  ... 
doi:10.26493/1855-3974.2320.c2d fatcat:ufr5bteqovgovdc2vapxky5jvy

A Practical Algorithm for the Computation of the Genus [article]

G. Brinkmann
2020 arXiv   pre-print
We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms.  ...  The aim of this algorithm is to be fast enough for many applications instead of focusing on the theoretical asymptotic complexity.  ...  For these tests, for multi genus no lower bound for the genus was computed.  ... 
arXiv:2005.08243v1 fatcat:eiibn3s44zctle4mp223tehbvq

The Graph Isomorphism Problem (Dagstuhl Seminar 15511)

László Babai, Anuj Dawar, Pascal Schweitzer, Jacobo Torán, Marc Herbstritt
2016 Dagstuhl Reports  
A highlight of the conference was the presentation of a new quasi-polynomial time algorithm for the Graph Isomorphism Problem, providing the first improvement since 1983.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 15511 "The Graph Isomorphism Problem".  ...  Tinhofer noted that isomorphism testing for compact graphs can be done quite efficiently by linear programming.  ... 
doi:10.4230/dagrep.5.12.1 dblp:journals/dagstuhl-reports/BabaiDST15 fatcat:meig4kvcgffnjiq5wpa6wjs6am

Fixed-Point Definability and Polynomial Time [chapter]

Martin Grohe
2009 Lecture Notes in Computer Science  
A property P is definable in L if P = P φ for some sentence φ of L.  ...  Example Connectedness of graphs, satisfiability of Boolean circuits, the language {a n b n | n ≥ 0} 6 Abstract Logics A logic L consists of a set of sentences and a semantics that associates a property  ...  Application to Isomorphism Testing The k-dimensional Weisfeiler-Leman Algorithm (k-WL) is a simple combinatorial algorithm for testing isomorphism of graphs, based on an iterative "color refinement" on  ... 
doi:10.1007/978-3-642-04027-6_4 fatcat:qajggupey5dq7gnn6mp2ehekny

On the genera of polyhedral embeddings of cubic graph [article]

Gunnar Brinkmann, Thomas Tucker, Nico Van Cleemput
2021 arXiv   pre-print
that number of vertices, and that there is no bound on the number of genera in which a cubic graph can have a polyhedral embedding.  ...  While these results suggest a large variety of polyhedral embeddings, computations for up to 28 vertices suggest that by far most of the cubic graphs do not have a polyhedral embedding in any genus and  ...  (a) What is (a good approximation of) the upper bound ζ 3 (2g) for the number of polyhedral embeddings of a cubic graph in a surface of genus g?  ... 
arXiv:2008.09467v3 fatcat:lhjvaviqtbey3fh423rjykbi24

Graph Isomorphism Restricted by Lists [article]

Pavel Klavik, Dušan Knop, Peter Zeman
2016 arXiv   pre-print
: for trees, planar graphs, interval graphs, circle graphs, permutation graphs, bounded genus graphs, and bounded treewidth graphs. 3) Algorithms based on group theory do not translate: ListIso remains  ...  NP-complete for cubic colored graphs with sizes of color classes bounded by 8.  ...  Bounded Eigenvalue Multiplicity. The polynomial-time algorithms for GraphIso of graphs of bounded eigenvalue multiplicity [6, 22] are heavily based on group theory.  ... 
arXiv:1607.03918v2 fatcat:rea4gbmazrbebbirsyhndky7mu

Fixed-parameter tractability of graph isomorphism in graphs with an excluded minor

Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Saket Saurabh
2022 Symposium on the Theory of Computing  
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph 𝐻 as a minor can be solved by an algorithm working in time 𝑓 (𝐻 ) • 𝑛 O (1) , where 𝑓 is some function.  ...  bounded treewidth.  ...  There, the goal is to obtain an isomorphisminvariant tree decomposition of the input graph of width bounded in parameter; then, to test isomorphism of two graphs it suffices to test isomorphism of such  ... 
doi:10.1145/3519935.3520076 dblp:conf/stoc/LokshtanovPP022 fatcat:ablwm2hiyrdzlatyxi57ivtnje

Surface Split Decompositions and Subgraph Isomorphism in Graphs on Surfaces [article]

Paul Bonsma
2011 arXiv   pre-print
The key to these improvements is the introduction of surface split decompositions for bounded genus graphs, which generalize sphere cut decompositions for planar graphs.  ...  We generalize this result, by giving an algorithm of the same complexity for graphs that can be embedded in surfaces of bounded genus. At the same time, we simplify the algorithm and analysis.  ...  Acknowledgement The author would like to thank Frederic Dorn for the introduction to the subject and the many inspiring discussions.  ... 
arXiv:1109.4554v1 fatcat:xnw762xzhbalnovrz77sb5bsye

Surface Split Decompositions and Subgraph Isomorphism in Graphs on Surfaces

Paul Bonsma, Marc Herbstritt
2012 Symposium on Theoretical Aspects of Computer Science  
complexity for graphs that can be embedded in surfaces of bounded genus.  ...  The key to these improvements is the introduction of surface split decompositions for bounded genus graphs, which generalize sphere cut decompositions for planar graphs.  ...  Acknowledgement The author would like to thank Frederic Dorn for the introduction to the subject and the many inspiring discussions.  ... 
doi:10.4230/lipics.stacs.2012.531 dblp:conf/stacs/Bonsma12 fatcat:agte2kqezrbklpanbukiliyiiy

Recent Advances on the Graph Isomorphism Problem [article]

Martin Grohe, Daniel Neuen
2021 arXiv   pre-print
We give an overview of recent advances on the graph isomorphism problem.  ...  Our main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphism algorithms with a quasi-polynomial parameterized running time  ...  Graphs of Small Genus Next, we turn to the isomorphism problem for graphs of bounded Euler genus. Recall that a graph has Euler genus at most g if it can be embedded on a surface of Euler genus g.  ... 
arXiv:2011.01366v2 fatcat:drrbl2cx3zabtkxo75f6nc5jlq

Isomorphism of k-contractible graphs. A generalization of bounded valence and bounded genus

Gary L. Miller
1983 Information and Control  
A polynomial time isomorphism test for graphs called k-contractible graphs for fixed k is included.  ...  The class of k-contractible graphs includes the graphs of bounded valence and the graphs of bounded genus.  ...  Isomorphism for k-contractible graphs is polynomial time testable. THE BOUNDED GENUS CASE Here we shall show that grai~hs of bounded genus are k-contractible graphs.  ... 
doi:10.1016/s0019-9958(83)80047-3 fatcat:7hvtd2q4tnfn5drybtgqnxvvjm

Computational complexity of reconstruction and isomorphism testing for designs and line graphs

Michael Huber
2011 Journal of combinatorial theory. Series A  
In this paper, we study the computational complexity of isomorphism testing for line graphs of t-(v,k,λ) designs.  ...  For this class of highly regular graphs, we obtain a worst-case running time of O(v^ v + O(1)) for bounded parameters t,k,λ.  ...  Acknowledgments I thank Peter Hauck, Michael Kaufmann and Jacobo Torán for interesting discussions about graph isomorphism, and for reading an early draft of this paper.  ... 
doi:10.1016/j.jcta.2010.06.006 fatcat:vxiuqw6zrjeqjab74skehfucnu

Page 3092 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
In particular, a linear time algorithm for testing isomorphism of graphs of bounded average genus is presented.”  ...  Summary: “Recent progress in topological graph theory has shown potential applicability of average genus to graph isomorphism test- ing.  ... 

Tropically planar graphs [article]

Desmond Coles, Neelav Dutta, Sifan Jiang, Ralph Morrison, Andrew Scharf
2020 arXiv   pre-print
We develop necessary conditions for graphs to be tropically planar, and compute the number of tropically planar graphs up to genus 7.  ...  We provide non-trivial upper and lower bounds on the number of tropically planar graphs, and prove that asymptotically 0% of connected trivalent planar graphs are tropically planar.  ...  In general, there is no known efficient way to test if a given graph is troplanar, although an algorithm for finding all troplanar graphs of a fixed genus g was designed and implemented in [6] .  ... 
arXiv:1908.04320v3 fatcat:lyqr2hk3snhcxddafayfcxhh2u
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